Решебник (ГДЗ) Алгебра і початки аналізу 10 клас Мерзляк
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Решебник (ГДЗ) Алгебра і початки аналізу 10 клас Мерзляк

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Решебник (ГДЗ) Алгебра і початки аналізу 10 клас Мерзляк

Решебник (ГДЗ) Алгебра і початки аналізу 10 клас Мерзляк

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Решебник (ГДЗ) Алгебра і початки аналізу 10 клас Мерзляк Решебник (ГДЗ) Алгебра і початки аналізу 10 клас Мерзляк Presentation Transcript

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  • 11) r'+ 3i. + 4 > 0; r, - 8rc - 4 < 0. r{icna ( 1) i 4 e xopeHnMn rplrqnelra x'z-3x-4, re (-1;4). Bi0no6iAb: ( li 1). 12, O,2t'> 1,8r; 0,2r'.- 1,8x > 0; O,2t(t 9') > 0i .jr € (--; 0) u (0; +-). Bi)noqi'b: (--i 0) u (9; +-). 2. niAMHoxrHa, Onepaqil HaA MHoxnHaM!l 15. AiBqara niAMHonnsa l.r$iB Knacy. Xronqi niAMEo)r.iEHav-rEiBruacv. + -t,,,--=-/---+ 1 --=----'-:------+ ---i 1 25. IiAMHoxsEIr: a; tl, 2i l1t 2]l. 26. nis;Hoxlrrra: o; { 1}; {o}; {1}; { 1; 0}; {-1; 1}; {0; 1}; { 1; 0; 1}. 27, I]paBrnbEe rBepAr{eHsn 3),60 a cdrblrnii e,leMeEr ABox MHo){ixE i neperI-I soM aatrlrx MHo*iIrH e MHo)icI{Ha, slla Micrur]' qefi crirLrlllfi eneMesr' 28. 1) {2; 8}; 2) 14; 7i 0ll. 29. MEor*(&si A ^ B Ha,reFiar6 'rr'tcra: 11; 31 30. Hexan.4 = {1; 2; 3; 5; 6; 15; 30} - Mflor*{IrEa AinLEr$iB 'rrcna 30, a B = {1; 3; 5; 9t 15; 45] - MEo)IllrIIa AinbH[KiB qficna 45, roAi A ^ B = {1; 3; 5; 15}. 2)A^B=A; 4rA^B=12;3,5,7]]. yqEi, rqo caxorlnlolorbcs Oyr6onoM e niAMHonrrHoro yqEi3 Knacy. 16. npoMiEb; liApisoR. 17. CerMeHr: ceKrop. pa,qiyc. xopra. 14. 1) MEor{vtra 6ynB croBa 4kopar € rinMso}iinHoro MHorrrHs.4. 3) Msonusa 6y&B croBe <Rapr{Ha' € niAMHo}I$rHoro MHo)ro{Er.4. 5) MHotrixsa 6yKB cro € niAMnoxrlllrolo MEoxnIIn A. 6) MHon{r.rHa 6yKB cnoBa (rrrpErD e riAMHomllsoro MHorKrHr ,{. 7) Msofiir.rHa 6yriB croBa (rrn' e ri.qMEo)rcrHoro MIIo)&nHr,4. 11) Mlro}rislla 6yxB cnoBa <Aapr € niAMHor.trHoro Mnon{r.rHr.r -4. 19. 1) Talr, 60 qrropu qncna 98 € eneMesraMs nnoxngn A = {1; 9t 5; 8}; 2) lIi, 60 ql{Opa 0 qrcna 9510 Ee € ereMenroM MHox(}rHv A; 3) raK, 60 qrropr .rz cna 519 e ereMeEraME M]]oxv au -4; 4) raK, 60 MHoxcrEa IIrQp.rrcra 5858 Aopir*o€ MEo,IurIIi {5;8}, sria d niaMnoJ*rrr, HoIo MHox'{Hx,4; 5) rax,60 Mnomrura qlr&p qlrcna 195 888 € MHoxrI{a {1;9; 5; 81, rxa € niaMHo, xnHoro vuo)+(fifix A; 6) ni, 60 qtopa 2 .rncna 91 258 He e eneMeHroM MHo)krIIr.4.. 20. Hanpxx,lai: AcAra A.-A. 21.Ilpaen,rrne raepA,*ieHHs - 2),60 MHo)IrgHa {dl Micr6rb € 'reMeHr a, nK fr€ sMEo- xnni {a; b}, iHEri rBepAx{eHH.s He € trpaBlrnEEr-rMr-r. 31-1)A^B=A) 3) 1 /l B = {19; 3A; 57, 76t 95h B) rpoMiE6. 2) (--; 3) - (1; 4) = (1; 3); 4) N ^ ( 3; 41= 11,, 2; 3i 4., 6) (-1; 1l ^ t1; +-) = {1}; 8) R. (-2; 3) = ( 2; 3). 2)(--i1)^N={1}j 4) (--; 7) n fi = ( *; 7). 22, A c B qe osHaqae, u{o eneMeHT[ Mnorr(ruI{,4 e eneMell- TAMI MIIO']iI{HI B. B cC - qe o3Ea.ra€, q B e eneMeHra- Mn MHornrHr.r C, ro6ro eneMeHrr MHoJr{n!I!. A € eneMeHraMr MHonir.rHn C. GincHo, snqo , ereMe:rr MHo?nnHa 14, ro s yMoB{ -4 c B BrnnrBa€! rrto, € B. gRrr{o r e B i E - C, ro r G C, 10610,4 c C.) 23,lrCcAcDcB; 2)B.DcE.AcC. 24. r) /,-;- ', ,/;-- a9@232 ll:l: A'I|EEPA Mep3nrK A. r. ra iH. A(a,qeMi.rHnr pieenr il:ilil:jlljli;i;ii AD ""''' ^r"K " u<1, "' 7r.2,,< .l ,--- =i1, ^- " ^141, i:.?.i:l. . :,:i::ii{* .:.ti:.itit .:n::::illt I n'At, 'xx'"Yl( ^L+)" ,1Y. 33. Ileperr.rHoM aBox rpoMesiB, rqo nentarL lra oAHiii npsMii, Mo)<yrl' 6vrr: 6) Bj.qpi3orii 34. 1) [-4; 6) ^ (-2; 7) = ( 2; 6); 3)( -;2)/r(3;8)=u; 5)( 2;2)^z={ ItO;lli 7 ( | 11. (ti +-) = a: 35. 1) ( -i 2) ^ rr' = {1}j 3) t 1; 1).j z = {-1i 0}; 36. flpasnrEne rBepatrcenEs - 1), 60 o6'eAHarns ABox MEoJ*{xs e MHotrctiHa, sxa Mic- TI,ITT, E'EMEHTI sAAAIIfi 37, 1) MEo)$nEa qrsp .rqcna 2? 288 € MHorxwta A= 2; 7; 2; a) a:l = 2: 7; 8)' a MHo- r{r(Ila qnsp qrcna 56 383 e MEo)rusa B = {5; 6; 3; 8; 3} = {5; 6; 3; 8}. 'fop,i A J B - 2;3; 5; 6; 7; 8). 2) MEorrclrrla qrop q!rc,!a 55 555 € MEoniEra -4 = {5i, a MEo,rcnHa rlq(Dp qrcna 777 777 e MP'ol'ujda. B = {7}. ToAi,a Lr B = {5; 7}. 38. l) A L A MHor<tua piBHo6Fapesxx rpyrl ffiYXiB 2) A u A = N{1}, ocftirL}$r Bci q'c,!a Earepar6Horo psav, oftpiM 1, € a6o trpocrl- MrI, a6o cftraAeHqMlt. 3) -4 u B = B .) {2}, oc&i"rbRl, Bci npocri 'r]rcna, oitpiM 2' e EerapIrI'rMI'r' i::iai{i::;::;iiit: AITEEPA Mep3reK A. r. ra iH. AKaAeMi'{Hni piBeHb:::::i 233
  • {r )" t' L" o' t;r; Ii frj iti. rl:i i:: li: li,::l ffi 39. 1) 06'€aHasHsM M,BC i AAC, e qorfipwiyr- 'I'rE ABCD. l>"t,/t,/ I ol o 2) 06'€anasHEM AA-BC i A-4CD e MBD. ,r/A" /,-'" .4 -B 3) 06'eAnaHnsM 4,4-BC i ADE-K € nlecrffiyr- Erk ABaDEK. l6a+320. l6x:-3.44. l) I I Li-4r<?; lar<0; BianosiAb: @. +*1. ". lar.+19:51 1. Jrr 20, ' 110x < 3x + 2l L7r < 21: Bid,ld6trbi porB'r3riiB HeMae. r>20- x<3i 06'€AsariHnM rprrcyrr]IldB He Mor{e 6yrlr BiApisoli, 60 06'€aEaHIItM }l{nHa, sKa Micrur6 €reMeHrIr noniHoi 3 AaE' 40. O6'€AHaHr'nM ABox ipoveEiB, ulo nen ar! a o.qHiii rp.aMin, e rptMa, npoMiEB 41. 1 ( 2. 5l'r (2i 7l = ( 2. 7lt 2) ( -i 3) L, (-3; 3l = ( -; 3l; 3)( -i8)u[ 2j+-)=( -;.]--); 4)RJ( 7i2l=Rt 5)OL,N=Q; 6)RL,N=-4. 42. 1)( -; 1lu[1;+-)=( -; +-); 2)( -;5)u(3i 5]=( -; 5l; 3)RL, Q=-4; 4) (5; +-) .JR-R. BnpaBn anq noBroPeHHc r 4! a -4' rrx 4l ly=0,43 lr _ - _ : " .''-0: ''' 0: x-4 r | !-1 ! 4 x 4. o {;',-J-u= o' Po3B's':*{eMo piBHsIrHs 12 +' 6 = o; SEanaeMo posB'.r3r.r.r HepiBHocri .!'+ jr 6<0; xe l-3.21. x= 3a6o t=2. +. + zt -i 5 -'8., rr'r,3)-ilr 3r-18 o; . 3 ir-3 r I (r-3XJ iJ) r'+3J. 5ir+15-18 (r 3Xr + 3) =0; x'-zt s -=(r: (x 3)(r + 3) BiAno6iAb: L x' 2x-3=o. (j.-AXr.+3)r0; l;,';,=" d o r 4 _I o, '',, ,r' t-i i r u',r-tr rt rrtrxr I r 4{l 'r l2rir..-lr.t.r lr' o. 4-4x-2, 2 x'z 2x l-o. trr')(l jr) {i-lrll rr [t' = t, t-4r,5 x -4r 5 'lr 4i' 5=0 1' t' ,''',,i-', =o',' ,'',,-i'=o'1,'-J,, ',,0, li,, ,. " 5 l*"r,BiAnoqiAb:'5. 12 2 3 l2+2tr 5t 3rir ll ^4)-U: r.r 5rtr r l) r'l , 5 (.r 5X' ri) 12 2jr-10 3r 3 o. tl- O, t'l- 0, {r 5l,r - lr {x 5jl,r l) (ir 5){.' , l) t+1=0: lx=-l: l" s . o. ]t, = s. r-h.rev? H.cjvi.Ha. l"*r*0, l"*-t. Btdnoiob: piBH^ Hq HF Mdc porB q'{is. 234 r::.:::: AtIrEEPA Mep3ncK A. f. ra iH. AKaaeMi,{Hr4i piBeHb i:l:i:':;:!;i':':li:i::: ,!> 0 i 4 > 0, ro6ro r.'z + 4 I 0. B'dnBib: *i--. 4) L.n1- 4x+x 2 5r-2 ')c2rr2:.(x-2 Ileii Brpas Mae 3Micr, sRr{o r(r - 2) + 0, ro6roJ. * 0 a6o n + 2. BiAnoqiAb: t*t 0) ,J (0; 2) u (2; +-). sf 1f- 2". IIefi Bupa3 Ma€ sMicr, .alirqo 6 7r > 0; 7ir > 6; (6 Bidnaqidb: -rl7 ,a97 r'. : + Pors r,l{pMo cxcrcMv: I - 3 2 " lr '0: o<r<2. BianosiAb: Q; 21. 1rr-r-12>0. 4t l 110 3r r' > 0. l. Po3B'-{}I{eMo HepiEHicrB r.'z t 12 > 0. ItopeFsMx rpx.rreHa re - r. - 12 e qtrcra 3 i 4; ,€( *; 3lu[4;+-). 2. PGB'flr€eMo HepiBlricrb r'z- 3r + 10 > 0; r'j + 3r - 10 < 0. ICop€HsMu rprqneHa .r r3x i0c q,,,nd 5i2ix-t 5;2). [' :. BpaxoBy'o'rH yMoBu (l) r (2). va, vo: r - 4: 5 tr- 2- MaeMo:r€ ( 5; -31. BiAnoBiAb: ( 5; 31. 3 5 45. 1) Brpa3 j- *u" ".i"', rlr]]lo r + 5 + O, ro6ro.r + 5. Ja+i) BiAnMi}b: ( -; -5) u ( 5; +*). r+4 x+4 2)Bupa3 +=. : Mae 3Micr, siirro (r 2r(r + 2 + O, totuo x t !2.' x' 4 k 2)G+21 Biano1i1b: ( -; 2) 'J ( 2t 2) u (2r +*). 3, Blipar ', - va. rvi'1 llp .r - R.60 x - ,l 0, ta.)vd roa.Hgi0 x-+4 :i::iaii:::::::iii: AnrEEPA MepsneKA. f. ra iH. AKa,qeMi,{Hhn piBeHb i::i 235
  • ll i 3t,;::i :l l:.i ,i :.: :i .!!ii! :,1:::::f il:ii.: ./3' + 6 BiAno6iAb: G2t +*). 7) J5-*,-+. qen supac mar rMirl. !.!-u 3Jr ,r ' roi ;t. . a----'-iBiAnosfib: loi 51. u b g J7 x - 42 - ' U.u u"0," r,ra. rMicr, sxuro r' Rr [r: e: ][- - o. - ,e lo: a)urar +*t. [x*sr [6; 8)u(8;+-). s) l|'' + 3' + a. 4en Br.rpa3 Ma€ 3Micr, sKqo r'2+ 3r+4>0; x' 3x - 4s0|' r e l-1; 41. BiAnosiAb: L I; 41. lo. -:::L. ucii supaJ,ra. JMicr, Jt' + 4x 12 sHqo ir'z + 4, 12 > Oi x e ( -; 6) u (2; +-). Bi0no6iA6: ( -; 6) !, (2; +-). f(i.) = - -Ar' + 2x = l;-$t2+2x+ 1= 0; 3t'- 2,. 1= 0; D 4-4 3 {l) 4*12=ltj: x, '--n=r,, t:o -} = -',oo f(r) = 56; 3f +2r.= 56:3x' 2x+56=Ot D=4-4 3 56-4-672= 668<0 PisHslrHs Ee Ma€ AiiicErx KopeHiB. 3)l(-1)=-s ( t)'+2 (-1)= 3 2 = -5. Pisgicrs l( r) = 5 - EenpaBIrnEEa' f(2 = -3 2,+2.2= 3 4+4= t2+4=-8. PiBHicr6 f(2) = 8 - rpaBI'nEEa. 1a rr i1+y=r=rs, i(o)=oq= o; lor=f|=f =:; y1-"1= 1L=19=-3, 33 -6 2) rJ-st =s; 3==t r-3=2;r=51 ir,l=0.s, 4= ];' - B = 36;,= 3e; l(r)= ro: -1L=-10; a=-s;'-t= 3' '=z-rlt 48. 1) @yH$ailo Ba{ario omcoM. J5 x>0. Jx<5. lr'o: [x'o; ]zx +z>0. lzt>az. lx' a,r * o: lxtx 8) + 0; ' = r1 t' = r.zr. nt J7 * s' tt ;1*. u"n ""0* "a€ sMicr, f*qo {'' ' s* - tr - o '. ,-, -7) .l2t 7)t zt .*). J{r 7l(r + 7) + 0: BiAnosiAb: ( *t 7, J l2t 7) u (7; +-). tzl , '*2 * =-. U"oBnparMa, JMicr, J35 + 2.r r' J8 - 4ir 35+2' x'z '0. [*' z' :s.0. la-+"'0, la*' s, Itr + 5xr 7r < 0. 1 xE(21 7). BianosiAb: / 5; 2. 92. noBTopEHHc I po3ul1,|pEHHc BtAoMocrEf npo ovHKqtlo 1. OyH(qit ra riocHoBHi BracrrBocri 46. f(r) - -l,'z + 2,. 1) l(1)= 3 1'z+2 1- 3+2=-1;l(0)=-3 0+2 0=0; rl 11.-r.l 'i-r.'-=".!.?=!,2-t n2t B.t2rt2 t2t lr/ 13/ 3 9 3 3 3 = 3.4+(-4)=-12-4=-16; l----.,-'- --:-:7::r:::11 -62- 2) E(l) = {0; 1: 2:3i. --- + -- ,.--=-- ,--- + ---,+""""":7 i)-i""r' 3) 2 23 1,7 5 -1,84 g 2 5 0,5 0,4 y = uE * z = "8 = z: 5 = G + 2, 25 = ! + 2, ' = 231 s=,1 r.ts' 2=u62r o.s; o.q=G*- 0.16 x,2,.r=-1.84. 51, @irypa r{e Mor{ie cnyryBarl-r rpa{DiKoM OyAlcilii, 6o sEa.reHlrsu t > 0 BiAroBiAae aBa ssaqesris y. 52. 1) l( 3,5) = -0,5; f( 2,5) = 2: l(-1) = 0; l(2) = -1. 2f(x)- 2,5, roMy ' = 5; l(r) = -2, roMv r = s,5; l(n)=2'roMvjr-0. 3) E(f) t 2.5: 31. 4) l(*) = 0, .ssrqo ;r = 3, x = 1, t = 1,5. 5) ftr) > 0, sxrqo ' e (-3; 1); J.e( 1;1,5); l(r)<0, sr{rxo.rL t 4: 3): x( (1.5: 51. 6) @ylrllqifl l(r') 3pocra€, sxqo jr € | 4, -zli t e [ 1; 0l; Ovlrriqin l(r) cnaaae' slrlrrox€ [-2; 1]; re [0; 5]. 7) a) Ha rpoMini&y [1; 2] OyHliqin l(n) nprfiMa€ EaiA6inL e ssaqeHHs, nxe aopiB Hro€ 1, ra HaiiMeEure 3lraqeHlls, nlle aopiBHre ( 1). 6) [-2,5i 1]. Hali6inbure 3Ea.reHss OyHllqii l(') AopilHlo€ 2, a Eai:iMerlxe slra'{el]- Hs AopiBEIoe 1. B) [-2,5; 3,5]. Haii6inr,ne 3IIa''eHHs 'rellEn aopiBHloe ( 2). ii::liiii:i::.::Ji:i AnTEEPA Mep3ne'( a. -i-_ i,/-':- ,.- X_ l- ii--- -57' tl -::--i::-:-r:$+ i2r 2 3 OvHKlrii l(r) AopiBnro€ 2, a sanMeHne 3Ha- f. ra iH. AKaAeMi,{slaf piBeHb ii:l 237 16 17 18 l9 20 21 22 24 0 t 2 3 0 1 2 3 0 2 1,2 16 g 5 2 2,4 -5 236 ll:i aITEEPA Mep3neK A. r. ra iH. AKaaeMi,rHnr pieeru l:i!{:i:ilii!li{:i
  • li1: l,tE; fi ::r :i .] :.: ;r 'i.:{a:' .!i:.:.:L 53. 1) l( ,{) = 0,5; ^ 7) = 2; f(1) = 2i f(2,5 = o,5l 2) x) = 1, roAi t = 12; flx) = 2,'to4i x = !1, 3) n(D = t 1; 3l; a) l(r) = 0, nlirro r = 3, r= 1,5,x=1,5,:t=3t 5) l(r) > 0, J{Krr{o r € [ 4; 3),r€ (-1,5;1,5),n€ (3; 4]; l(x) < o, .sr{qo r € (-3; 1,5), J. e (1,5; 3)i 6) n(qo r e [ 2;0]ir€ [2;4], 10 rDyHl{IIia flr) 3pocraa. .'IRqo x € [ 4; 2] i x € [0; 2], ro qryriHrri' l(r.) ctraaae; 7) a) [ 3; 2]. HanMeHue 3lraqeFEs (Jyrnrrii l(j') nopirHloe ( 1) Hafi6i"1b e 3Ea- qFhhr +t Hs '11 /(ir) nop:8hrc. 0. 6) t-3; 11. HanMelrtlle 3HaqeHHn dryHFrrii l(x) aopinHloe ( 1), a Eai:i6irbrre 3Ea- .reHH'r -- qncno 2. s) [ 3; 1]. HariMeHDe 3tsaelrH.s dyEIiIIii l(ir) aopiBErc€ ( 1), a Han6inlue SraqeH qricro 2. 54. 1) O6,racrlo Btr3Ea'ierllls $yHftIili ili = : . e Bci rilicHi 3HaqeEss J., RpiM .x = 4. r-6' 2t ftxt = : . D(f)=R. s) /(r)= -j'-i: Dtf=17:+-)t 60x 7>0, rliqo:,.> 7. lo 4r /tr.r= ' ; Dl,t) { -i .1,;{ r I 0,J lr. J-x 1 5) /(:r) = Jr' + 6:lr - ?; ,(D = ( -; 7l'Jl:rt+*), ..1.....- 60 jr'+ 6jr ? > 0, sftrqo n € ( -; zl, iir r-r. i -a1 61 /tir) = --1. SHa.reliHt OvERiIii l(r.) icHy€, nlrll{o tr 5it I 0; r.(r. 5) + o; r.+0a6or+5.ToMyr(r=( *; 0) ! (0i 5) u (5i +-). l 56.1, l(.r)=lr 6. flxrqo x = 0, ro l(0) = 6.Toqna(0; 6) - roqlta repeausy rpa Oirla cpyg,iqii l(r.) s Biccb oy..tlntqo l(r.) = 0, "o lr-o=0, ]-r = s; r = +2. To'r''77 Ita (42; 0) - roqna neperrsy rpaoi(a OyHrirrii f(r.) tu Bicclo Or. 2t ht.r=1?* T ".*" x 0. ro iro, 2.4. nr(uo irrr " o. . lf- 3j o. 12+3r =O- r=-4. robro - 1 Orxe, roqI{u (0t 2,1) i (-1i 0) roqr{u reperlrliv L2.r-5*0: Lr=2.5. rpaoi(a dryHlluii '(J.) 3 ocsMr' RoopaxHar. 3) s(,r) - 5 - r'..ERlro x = 0, ro s(0) = 5. flI{qo s(r) = 0, ro 5 - I,= 0; :r=tJs. orxe, roqru (0; 5), (-./6; 0) i ("6; o) roql(I{ nepernFy rpaoim rDyllrtqii s(r) 3 oc.aMn rioopaiEar. a) o(.r)=rE 2. flfiqo jr = 0, ro (p(0) = 2. fll{tqo 9(,.) = 0, ,o Ji z=o: G =2, .r = 4. Orr"e, roqKr (0; -2) i (4; 0) roqftr neperrny .paotua Oyxl{llii I (.r) 3 ocfl- MrI Koopartsar, 57. 1) l(r, = 5f + x - 4. gnqoJ. = 0, ro l(0) = -4. flliqo l(.jr) = 0, ro 5r.r + r - 4 = 0i D I 4 5 l-41 8l:.. ''0,8; , I OrxP. roqHr(0: l). r0 lo t0,8; 0) i ( 1; 0) ro.rKr repeusy ryaoi(a oyHllqii l(r) 3 ocsMl't (ooparHar' ": .r" ly 3r 0, 2) ^rt ' '"-. fl*uro )- = 0. n /(0) 0. flKUro /r.rr 0. o 1'' --"r a l' 8,0: lrrx 3t o, lx 0, -I roq*" (0:0) i( 3i 0) roqKv n"oel ,H rpa0"{a tlryHKqri Lx-8i l'= 3. 3 ocrMrr rioopArHar. 58. 1) l(r) = o,ai' 8; 0,4.r 8 = 0; o,4r = 8: x = 2O; 2)s(xr=2a+3:. ," -r2 +3x+ 28=0; rr 3r-28=0; D s 4 t r.28r 121: r. 3-I1=7. "" 3 ll 4i 22 3),r(r)=v[+4; .it+a=0r r+4=0; r= 4; r'z+r 30 4) $lr) = ---; 5) flr.) = r.3 9r; ;rr 9.r = 0; n(irr 9) = 0; r = 0; r. = 13i 6 eQ) = a' + 4; tc') + 4 = 0, r e Q. 59. l) /(/) rr 1.r; rs-1"=0, ' 4;. o.xe. /(xr=u. nx.uo t 45. '33 2, flr = 5r' + 4x 1;sx'z+ 4.r - 1=0j D-2 i., rr-4.5-9: '. 2*3 l, ".'3-l I. 4555 O,Hp. ^jr) 0. flKULo r 0.2 i x L a) l(r)=rf,'-s; uft=o; r'z e=0; .r = 13. or'Ite, ^') = 0, sxqo ' = i3. 7) /(x) = ,6 + .f1 ;. sHaqeHss OyHKIrii l(Jr) icnye, srrtrro ro6ro 0 < a < 1. ToMy r{l) = [0; 1]. x a.0. 1 r>0; r>0, J'- o, [:r < t; 8r /ri) . 3 "'FHIs +]hKuii /r"r rrHv.. qKuo 12 4r x' Oi Jl2 4x x | 4x-12<O; 2<r < 6. ToMyD(/)=( 2;6) ,) l(') = *+ sEa.ienH'I oyHnrrii /(r) icsy€, 'iHqo To6ro r - 1 > 0, r:' 1. ToMy r(l) = (1i +*). ro) l(:r) = G J r. sHa.{eErrs Ov"xqii f(,) icllye, rl{rlo To6ro r = 0. Touv ,(l = {0}. 55.r,/(r) '1.otn (-:2) t2i -)6('x,2.' t+2 I 2t ltxt , "6.Dtlt R.6o-t rI 0norr R- 3) /rir) 3j 2 . g.ro r 5r - 4 , 0, ro rlaqpHHt /(r., j.q).. ' r' 5r+4 'roMv ,(f) = (-*; 1) u (4; +-) (6onpr.r= 1i:,.=4srpasr: 5, +4=0). qrfrr, u6rz r 5.D,/) ts,r-r.oo ]i l, l i," t 238 r::::i AnfEEPA Mep3nqK A. f, ra iH. AKaAeMiqHnf pieers j:l:;:i:;:;:i:;:;i:il:ii Orri{e. flr) - 0, sKrro r = 25. :;:i:::i:::::::!::::::i: AITEEPA Mep3reK A. r. ra iH. AKaAeMiqH{r piBeHb :iii: 239 Jr-t>0, LJ. 1+ 0. 4f(r)= 4trea. 5r frrr=5-02'r ! -0.?{ = or a-2 x 2 5 0,2J. = 0, x 2+Oi x=25,
  • 0) l(:) =.r'? + ti t2 + r = O; r(r + 1) = 0; r = 0 a6o t = -1. Orxte, i(t) = 0, rlcqo r=0,r=-1. 60.l) g = 7t 3. npoMixHr.r rHakocra-flocri: y > 0, snDro -7t + S>O; 7x> -S; x<!;7 y<0,filtnto ?x+3<0; 7x< A; x>?; 2) V - x' at + 16. flpoMbtrrrlr 3EaKocranocri: A>0,f 8r+16>0',(x 4'>O,t+4:xe ( -;4) u (4; +-); y<O,tea. 3l , 6 floori**" rgarrocranorri: ' 4-a v 0; =Lr0;4 x 0:x 4itc @i4)i"4t u.0; " 0i 4 r 0;x 4; x-(4t -). 4t ! x' L npoMiAkl.r 3Haxocranocrj: A>O| *+ 1> 0; (1 ,X1 +t)>0; y > 0, sroqo r. € (-1; 1); y < 0, nKqo t € ( -; -1) u (1; +-). 5) u = Zx'z 7x - 4. IlpomrNnr 3Hakocra,locri: y > O;3t2 7t+4>Oi3x'-7x+4=O,D=7''4 3 4=49-4a=Ii 7+1 4 1 7-l , r.=-=-=I : r^=-=l: '633'6 u<0.Uc2-7r+4<O; 62. 1) Hexan t, > t| Ma€Mo 10t, 3 10t1 + 3 = 10(t, - ,r) > 0 roAi 10r, 3 > 10t1 3, ro6ro OyHRqis y = lot - 3 e 3pocralo.{orc. 2)g= 3r+ 7. Hexaii ', > ,t, roai g(',)= 3',+ 7iy(r',)=-8tt+T SEaiaeMo: y, y,=-3r,+7 +3 7= 3(J', a,)<0 @vHriqia v(t) e cna'qnolo. 3) Hexan jr, > r,, ro,qi y(t,) = I 2'; a@) = 9 - 2t,, SEanaeMo v, h=9 2a,-9+2=2(t' x") < 0. ovnxqis v = I - 2jr € craAlrorc. 4) v = t, Hex ft x,> roaj. vk,, = r,t V@) = xr SHaiAeMo: y, yt= t,-(-rt)= 1 -.t, < 0. oyEftIlis y(t)€ craAHolo. ttll 5r y ;x. Hexan.r, r- rori !(x, uG. -r.- .r, =;{t, .Y,)>u. oyHRuie y(.r) c apocraloqoo. 6) V 2 0.6x. Hexaii x? .r,. roAi vk) - s(r..) = (2 - o,6x") - (2 - 0,6rf) = 0,6is1 0,6', = 0,6(x, - r,) < 0. (DyHKqii y(r) e ctra,qHoro. 63. 1)y= 2r+5 , . (--' ?-)' "(?'.-) y > o,.nxrqo r e t -, tr " (t|, **), y<0,'xrqo ".{.'''*J. 6) V = Zr" + 8Jc - 1. IlpoMi*{rin at u*o".-o"ti, .+- 11, ---+---- -],'- r ,r 'a ----,.'-i-/--------; --i-.j a) ,(t) = 0, sriqo -2r + 5 = 0; t = 2,5i 6) y > 0, "sRrro -2x + 5>0,)c<2,5, ro6ror€(-;2,5); A < O, t> 2,5, ro6ro Jl: e (2,5; +-)i B) OyHI(qis y(t) € cra,qHolo. 3) g=2 l]>0,re (-*;0);y<0,t€ (0; +-); OyEriqi.r y(r) € cnaAEoro. 6 a) 6) B) a>U 2f+ 3t- 1>0iy<0; -2x'z + 3t + 1 < O: -zx'z + 3x + 1 = O, D=s-4 (-2.( 1)=9-8=1; " =-91= r.,^ = -3n1 = 1=e.s. '-42 Orxie, y > 0, s&qo jr € (0,5; 1)iy < 0, €lcrro r € (-*; 0,5) u (1; +-). 61. 1) y = 0,6t + 12. IlpoMiri(u sHarcocranocril 0,6x + 12 > 0; O,6x> -12i r > 20. Orxe, y > 0,6Rtqo t € (-20; +-); 0,6r+12 <Ot0,6r < -12i I < 20. Orr{ie, y < 0, s&qo jl: € (--; -20). h U =,18 ' 3, tlpoMinxu rflakocra-ro.ri: y>0; G+3>0; r20. Ornie, y>0, sRqox€ [0; +-); g<OtreA. 3t g = 9x - x'. flpoMi)rrKr 3Hel{ocra-'Iocri: --- _/-T=,.- y > Oi 9t - t2 > O; r(9 -.r) > 0. Or!(e., > 0. ------1,-- i----- tl(qo r c (0: 9) i3, 0. txqo r.. ( *i or J (9i +-l 4l g 4x' 3x - 1. flpoMiJ{rHx 3saKocra"loc'i: u > O, axnto 4x'- 3x - 1> 0; D=3'- 4 4 ( 1)-25i ._ 3-5=r,, _3-r _o.zl. -->j--_}4 ^' s -' i' s -o,25 grinro r € (-*; 0,25)u(1; +*),rog> 0..Exqor€ ( 0,25;1), roy<0. 24o fli: AITEEPA Mep3rrKA. r. ra iH. AKaseMi,{srai piBet" {i;::li$tilrli 4) a)y(a)=O,reO; 6)u=2>O,xeR B) y(r) - crara OyHrcqis, rpoMir{RiB 3pocralll{fi i clla,qaEHs EeMa€. 6)y>0,a1cflrot€(-;0); y < 0, nREIo t € (0; +-); B) dysK4ra v(t) spocrae, sllqote ( €; 0)ixe (0;+-). ;:iiiiiiil:iillii uresPA Mep3nrK A. r. ra iH. A(aaeMi.rHran piBeHb ii::: 241 ag(x)=O,xeA'
  • t"iftiEt! El: ,ji :. i:l :l t.:.:.!!ii!l I.r:.ii!:.i:.: ti!l!!!i!i 5s=x'+2, 3 6) a=2r x' 65.'t) s = l(x) /(r)=0,flnrqof= 3i,.=4; 66.y=l(rc),x€[-6;5]. l(:,.) = 0, slinlo r. = --6, 67.y=f(r),ae | 5; al. 1).trl{qox€[5;1], 3pocrae; sRrlojr e [1; 2) !=e(J) e(:r) = 0, anrqo :t = 2, x = 0, :. = 3. 2) 'Iriqo., e [-5; -1] i [2; 41, Oyrr( qis cnaAa€. OyHriqis 3pocrae, n{rqo x e I t;21. a) y(r)=0; r.i+2.' 3=0i.r= 3a6o r=1; 6) .r' "r' 21 3 > 0, s(rqo r - ( -r 3) (l: --r: ir' 2.ir 3 0. srtrqore ( 3;1); s) OyHXITiE y(r) cnaAae, slcqo r ( -: Il. 'trvHK rq /,1x) 3Poc.a.. E(iqot€ [ l;+-). I 64. l) q=3 r 4 a) y=o,snrro r=12: 6) r> 0, flrirro xe ('*1 12; a < slrqo , e (12; +-); B) cpyEl{qiJ{ cEaaa€, sllnlo r. E -q. 3v= a"+ 4x 3 0, a) r=0,sl{qor=1ix=3; 6)y>o,ir€(1;3); a <0,x. ( -i 1)u(3; +-); B) dlyHr.iqin y(jr) spocrae, sriu.ro i. € ( -; 21, Oylrnqir y(.') cra{a€, snqo r € [2; +-). 242 ,;t* A'.IEEPA Mep3neKA, F. ra iH' a) y(,.) = 0, sErqo 2r r'= 0; r.(2 - rl:) = 0, ro6ro r = 0 a6o r = 2; 6) u > 0, s.asto 2x - x'z> 0; .ir(2 t)>0; r € (0; 2)i y < 0, nlirqo , e (--i 0) !, (2i +-); B) OyH:iqi' ,(J.) 3pocrae, nxrqo r € ( €; 11, OyIIIlqifl r(r) cna,qae, sklroxe [1;+-) al U=o, xe ai 6) y> 0, jr€ (0; +-); y<0, ir€ ( -i 0); B) rDyHnqis cnaaae, .snqo t € ( -; 0) i.T€(0;+-). a) 9=0, r=13; 6) y>0,'nnloJ'E ( 3;3)iy<o,sHqo jr € (-*; 3) u (3; +-); B) OvE(qifl 3pocrae, .sl(qo ,. E ( -; 01, OyHriqiE cflaAae, ERllo jr € [0; +-) AKaIleMl9H14t'l plBeHb,ii!i:.ii:.iiii: ; 6a.-r=/(r),re -R. (DynRqis 3pocrae, sl{uro ir € ( -; 2l i [0; 3]. (DyHkrrir craAae, Eri!{or€ [ 2;0]i[3j +*). dlyExrrifl l(x) 41, drylrl{qis r l" tro. lt,t.69. l) /(r, J,; I 1 Dllt l0; lJ (l; -);r I L.r-U: '-U:11 2) flx)=-+-i x'! 1 + O, x + :tl; r' + 3x + 2 + 0i x + li:t+ 2; a' I a'+3r+Z ,(/)=( -; 2)L.J( 2; 1)U( 1; 1)L,(1;+-); 3) ft"t= '!:' 2.1 t -r-2 4t It4 2"*1=15-7r- 2x l-3=o'' r-3 lttttx zt o: 2a'1 7x-15<o: : !x=o: 4) s=9 r'z ::iai;:::!iii;!lii: AIrEEPA Mep3nck A. r. ra iH. AKaAeMi.rHht piBeHh i:i::: 243
  • -1 J,-0, lo r>o Ix.o. [.r x>0: lili E: t;:l ii i i i:ri:.i!i!!: ]' " - o,tre.r. - I1.5:3r J13:51. 2x' 7x 15=O; D= 49 + l2O=169i 1+lA 7-15 3 --.rr=-=5: st ft'l=uE,4 *,1; s,. * 7: xz4. l2r 8>0. I llx<1. lr' 8r+720: l-_,tL^ _ 1--a r' 8x+7=0:1" " i,=1. Ofliie,r€ [7i +-). fr>0. 6) /rr) Jl,r -ir; lrl - r '0: I ^ a6o lx .r " u Orn|e,r€ ( -; o)Uf0i+-)=( -; +-)=R. l.r . o, ["<o 70.rr /rrr J*-r. 3 1r'l'0 1' '' o.*., !' I ti4) )t4: +-) a Lr 4,0: l.rFa. 2t [tr '- '-, 1' ' ", ., {f ,];x'-5x-4 lx +5x A' ..x, tt lr, 5.x 4=oiD. 25 16 .9: r.. - trt3 -,, ". - ';t -ot. Oxe, D(f) - I-2: -1)u( 1; +-). 4) i(jr) = l'l 3. o6,racrE 3Fa.reHb OysRqiI t(jr) = I 3; +*). 5t lt = J-x : Etr)= oj. 6) l(,) - !t-1 +!5-; t(i.]) = {o}. 7) f(r) = x, + 4x + 8t f(r') = (r + 2t, + 4. KoopArEarr BepurEq t" = -2, g. = 4, iBirrcr' rapa6orr cnpsMoDaHi Bropy, roMy E(a) = l4t +*. 8) /(t) = -r': - 2r + 5. ItoopArEarx Beprxtrnu napa6onqi l a= (-1)'-2 r'l).5 lr2 5 6. " 2.1 nBir(sr napa6ons cnp.nMoBaEi BHr.r3, roMy t(jr) = t -; 6l- 72. 7) f(x) = 4 Jrc; t(') = (--; al. 2) f(t) = t, - 6r; fG.) = A:t 6). ,"= 9=s,v.=-g,r(t=t s; +*). 3r [-x : 0' 3) f{jr) =./_-t ffi, ]+ ,,,0; rc E ( 2t 01. orxie, ,(D = ( 2; 01. ir<0, (2 r)(2 + r) > 0; l'< o' ) z.'.2; 2 16 x-o' t/6' d) /r.r, = 6 , , ,.' u-, l:"]r;";., ;,;1.,- r, ]l; :l; r. € { -i 0) u (0i 6). or}I€, D(D = ( *; 0) !r (0; 6). 71.1) f(i=G+2. Oyr.Errii I](,) = [2; O6nac1.L snaqeIIb 73. U DrlJ=R, Hpivr.=-2, r=3. HanprrKna,a: /t*t ,--..l-- -.(,r + z)(,r 3) 2) D(fl = ( q 31. Hanprliraa: l@) = Js - x. 3t DUt=l-4:5r t5: --1. Hanp KnBn: Ittl J'*.4 . 4) DO = I ll.Harpunnaa: n, = V' -, - "-j-, - r. " 74. t) D(f) ( *: IJ J ( 11 0) (0; 1,. Hanpr.aKna,q: /(x, (x + 1Xx 1)r 4 D(n = ( -;7). HaEprnnaa: ftrt = -!.J-,.? 3t DUt=l2i5r J (5: tjr L {tjr '-). Hanpnx,ran: /(.y) l: ' -.{x c)tx b) :iilil::ti;i::.:i::J A'TEEPA Mep3fle( A. r. ra irl. AKaAeMi,{Hnn piaenr lilj 245 3) l(,) = 6; t(,) = { 6}. 2) flx) = 7 x'|; E(r, = ( *i 71. 244 tii:: AJIIEEPA Mep3nrK A. f. ra iH. AKaaeMi.rHlan piBeHb ::i:::i::::::::i:::i::::j
  • 2) TaK. 3) raR.75. 1) Hi. lx+I.ekuox< 1. 76. ftx) ', ^ lr' l. sxuro .r : 1. l) f( 2= 2+1=-1,60( 2) sa,qoBonbsse vMoBv ir < 1; l( 1)=( 1F-1=1 1=o,60( 1) ra.qoBonbEs€ yMo 3yn> 1; /(0) = 0e 1= 1, 60 0 3aaoBonbnse yMoBy r > -1; f(2t = 2' 1=a 1 = 3, 6o 2 :a,qopoasn.a€ yMoBy x > -1. 2) f(x = o, .a(qo ' = 1; l(r) > 0, nKu{o, € (1; +*); l(r) < 0, sKqote( *; 1)L.,( 1;1). OvExrris i(jr) spocrae lra npoMirriKax ( *; 1), [0; +-). oylrr{qis l(r) cra,qa€ Ha npoMixrxy [-1; 0]. [r+6.rnuor< z, 77. tt ltx = 1r r x. sxuro - 2 1 "r < 2. [2 -.r. FKU{o .{ > 2. IpaoixoM OyEllqii Yr =, + 6 e rpsMa. (Birllnr crpEMoBaHi eropy, 60 d = 1, 1 > 0, rpaoiIi repernHa€ Bicb Or y ro.tEax ( 1; 0) i (2; 0), a Bic! Oy - y ro.rqi (0; -2). fpaoixoM Oy:rRrlii y3 = 2 r e npsLtd. l(r.) = 0, sltqo r = -6, t = -1, x = 2; /(r)>0,.sRrrrore ( 6; 1); flr) < 0, anrqo r' € ( -; 6)u( 1;2)u(2; +-). iDyHxuir rpo.lac r--: -2r i (l: 2|. l,Dyr.{uir coarac Ha ,povi1lr"ax I 2: ;li (2t *). [r:+2r.gxruo:<0. 2') IGJ = I lr.' - 2r.. eKuro r. > 0. fpaon{oM OyH}iqiii y, = t2 + 2rc i g2 = )c2 2t e na- pa6onn, (Birllr' nxrx crpsMosaHi Bropy, 60 a > 0, a nepfinrnaua e iovxr (-1; -1) i (1; -1) siaroBiaEo. l{r) = 0, sKu{o r = -2, r = o, z = 2. l(;r) > 0, suro .r e (-*; -2) u (2; +-). l(r) < 0, flflrqo r € (-2; 0) u (0; 2). oyn(qis craaa€ l]a npoMirn(ax ( -; 11, (0; 11. .Dysl(qis opocrae H npoMix$ax [ 1; 0], 11; +-). l8 I .rnax< 2. 78. ftxt = l2x' - a- qKlo- 2 s x = 2. ls ^ I .sr{4n>z. RR f pdoirov OyHRrrifi u, -- i !r, - .rilpp tx 6oJrrr, a rpAOi{oM OyH:1'i y,= 2tr 4 e na- pa6ona s BepIIIrHoro ! ro.rqi (0i -4). f(x) = o.,tr"DJo' = -2, k = 2. i(r) > 0, n}lqo r € (-*; -2) u (2i +-). l(r) < 0, sllqo r e (-2i 2)... OyIIKrris l(r) spocrae Ha rpoMidiEax (--i -2) i [0: 2]. OyHXuin /(i.) .naqac Ha npoMi]{Kax [ 2; o] i (2; +-). ro 10 79, l) u=-:-:-,.r L [2:5|. O)HKuifl 1/ :t' Bosa 3pocrae, roMy Ean6irbnre qe y(2) = 5. to 10 2) a = -, )c e lz; ol. oyurqra g = I lrenepepBlra, Ha npoMilR&y [2; 5] craaae, x.x aoMv sQ) =.5 qe Ean6irbrre BI{aqeIrHs, a y(5) = 2 qe IIaiMeIIllIe 3Ea.renHs. AO-g= t'+61 7 1) r E [1; 2]. (DyHI(qis ! = r'+ 61 7 - EerepepBEa, Ha trpoMiri{fty [1; 2] spocra€, rpaoiKoM e rapa6ona B BepmrEoro B ro.rqi (3; 2), iBirnrr cnpsMoBaEi Bslrs, 60 a=-1,-1 < 0. ToMy Hafi6inr,ure BEaqeHHn e v(2= 4+12 7=1,asafiuesme qe y(1) = -1 + 6- 7 = -2,6(r.' = 3 He Hane,'irrb rpoMi,riEy [1;2]. 2), € t1; 41. IIboMy rpoMix{(y Eane}I{'arb il: = 3, roMy y(3) = 2 € Ilaii6inblnuM 3Ha- .{eEHnM OyHxrrii. IopiBHneMo 3HaqeHHn aG) = -2 i a@ = 1. HanMeEtlle 3rra.reHHs vt) 2. :::::il:iiltti::lt: A'TEEPA Mep3nsK A. f. ra iH. aKaaeMi,{Hnr piE,eF.b iitlti:. 247 n. 5) Hi, 60 roai a,'ls 6yar,-sno.o sHaqeHEs , icHy€ ABa pisssx sriaqel]Hs y, lro He BiArroBiAa€ BnsFaqeHslo oyEnqii. ir ;:,iil:.i:.:.:{ lr:.!alt:.1.1n 1.:-':.i!]1i:.:{ l'ilt i.!i:.i-i:. ti:ii-l:.i!-ai:.: lt*:.i:llll FenepepBEa, Ea rpoMfun&y [2; 5] e aG = -2, a HafiMel xe 3HaqeII- IpaoirioM OyHKtIii U,= t" t - 2 € tapa5ona, 11 r -r 1 r sepuuHoo B'ro.,u.i Art 24) (t" 2=1. /tl'z t 1 I 1 = -l 1= - -2=-2--", 21 2 4 2 4 246 lii: AIrESPA.Mep3ncK A. r. ra iH. AkaaeMi,{Hrfi piEeHb ,iii:':,i;i:iitlil! 4) Tan.
  • 3) n e [4; 5]. Ha qboruy npoMiJ(I(y senep€pBEa Oyrliqis cra.qa€, roMy y(4) = I € Han- 6inr,mrM 3IIaceHHsM, a y(5) = 2 e safiMeslllr 60 x = 3 He EanealrrrL npoMi'{llly [1; 4]. 81-y=)t'+2, 8 1) , € [ 5; 2]. Ha rrBoMy rpoMixrRy oyrHrris EenepepBrra i cna.qae, a6cq{ca B€pIIIuIrH Mpa6orq x, ; -l He Hajexnrb raHoMy npoMrlr{K). rov} Ul s, 25 l0 8=-7 e Ean6inbme 3HaqeEHn, avC2= 4- 4 8= 8 e llanMeEnle sEa.reHlrs. 2, xe [-5i 1]. A6cqrca Bepr x r napa6oJrlI n = 1llane]iillrb qr,oMy rpoMinc&y, {sirKu, trapa6onn crpsMoBaHi Bropy, loMy y( 1)= 1 2 - 8 = -g e HaiiMeHrie snaqeElrs OyErsrris. flopiB$seMo 3Ee.reHHs v( 5 = 7 i y( 2) = 8. Han6inb e 3Ha- qelrHs - 4e y(-5) = 7. 3) r. 6 [0; 31. Ha qboMy rpoMir{rcy HenepepBEa ibyHnrriF spocrae, rs = 1 He Hane- rnr{rL rrEoMy rpoMi:riliy, roMy y(0) = -8 e HaftMeErrnM sHaqesEsM, a y(3) = 7 € Han- 6inErrr.rM sIta.reIIEsM. A2.l) g = x, - ta - 21, + 25if t to 28t2b Oi D - la - 2' - 4 . 1 ..25 = a' - 4a + 4 - IOO = a.'z 4a 96. Ans roro, rqo6 Aaxa Orflrlliis Mana ABa Eyni, rpe6a, qo6 o? 40 96 > 0. Po3B'g}I{eMo qro EepiBnicr!: a' 4a 96 = 0: D=4-96=roo: o.=2--i!=n o^ 2 to 8. 4'1 1 Or}r{e,.El{rqo a < -8 a6oa > 12, aalla ibynxqis y = t'+ (a 2'), + 25 Mae A3a Eyni. 2, a = 2x' + 2(a - 6)x + a - 2i %c' 2(a 6!+ a 2=o; (1) 2=g-Ay 2@ 2).o, tza t 36 2at4 ar t4aa 40. 4 D fllrqo:> 0, To piBHrEHr (1) Ma€ ABa Kop€Ei, a Cryrfl{qis y = zt'z 2(a 6r+a 2- ABa Eyri. Po3B'ndieMo HepiBHic?b o? l4a + 40 > O) a' 14a + 40 = O; 9-qs oo 9, o, 7-3 tot a, 7-? -4. =-,--:>6-' 4'1 ' tlpr o € ( -; 4) u (10; +-) AaEa Oynnqiot ru" auu rrv,"i. 10 t A3. 1, a = r' + (a - 1rr. + 1 - a - a'! (*li ''z+(a 1)r+1-a-a'=O (1). IIe piBssnHr Mae ne 6inblne oAIIoro llopeEfl, nKqo, < 0, a AaHe piBffrflra (*) Ma€ He 6in6tne oAnoro Hy,rs. D=(a t' 4.1.(1 a - a' = a' - 2a + 1 - 4 + 4a + 4a'z = 6az + 2a 3. PocB'&rceMo rlepiBtricr:. at + 2a 3 < 0. 50 | 2a 3 0; - l-5 (-3J=l-15=16; 4 ", =-]4=!=o.s. " =-l:!= r. -1 flpr a € [-1; 0,6] aalle &ys&qis (*) Ma€ se 6irL e oaHoro Hynr. 2) u -1 x" -sax -9a -8a (*J: '4 - 1 x' + sax - 9a' - 8a = 0 (1). 4 Ue piBEssEs Ma€ ne 6irErre oalroro ftopeHs,.aftrqo, s 0, a aaHe piBEsHEs (*) Mae HF 6irbure oruol.o Ryna. 248 til: AIrEEPA Mep3rqKA. r. ra iH. AKaaeMiqHrf piaenr i;ii:liiii:i:ilijl:l / 1 D 25a' 4 l +l I go' -aa)=25a -ga -8a =16a'1-8a; 4' D < 0; L6a'z - ia < O;84(2o - 1) < 0i + , + nDn a € [0; 0,5] naHa Oyll&qi.s (*) Ma€ He 6inbl]re -3----;:------; a4. a = L, h> o, x € (--; o) u (o; +-). Hexafi r, € (--; 0) i r, E (-*; 0), x, > r, (lr,l < :c1), roai: !. !. o'*.:...^' >0.60k 0. rt-x2 tr.a xr2 o {lr. Heiaii jrt € (0; +€) i r, € (0i +-), ,, > r| roAi: h -t =h(t" )>o,6('h>0,)r2 x2>oixf2>o (2). xtt" 3 yMoBr (1) ," > r", ^rt L, L. rt xt B y,l,oBtt (2) a" > r", un" L , L . orrrre, Ans t, > ,r MaeMo V, < y1, ro6ro C = L op, * > 0 cnsqa€ Ha npoMix{Kax (,-; 0) i (o; +-). ,=!. u. o.r.c r-@:o)u{o:-a) HexaEt,€ ( 6; 0)it,€(-;0),r,,r,(t,<n,),roAi k -k =k(" '')<O, 60k<O,x, ,r>Oir1r,>0. MaeMo: x, < xz i r(r,) < y{x,). ro6ro ,=L, U.O Bpocra€ lra rpoMi'Iiriy ( -; 0). Hexan ', € (0; +-) i ', e (0; +-), x, > ,"""^, +-+=u':,;''t <0,60*<0, h az rt> O i rJ,> O. Ma€Mo: rr < r.? i 9(.tr) < y(x,), ro6ro y =:, k.0 spocra€ Ha rpoMinRy (0; +-). 85. y = i(r) - ctra,qEa Oylrxqis. 1) a = sflr). IJexan i x2ha.re:!l,aat D(g) i x2> tr ron1f(r,) - gf(t)= 8(flt,)- ^x,D <o, 60 f(12) < f(t), ockuttLn f(t) cnaAsa abyEnqis. Or*e, y = 8l(x) - cransa OyEx- qi.n (3/(r,) < }f(x) 'rp*r x,> xr x,e D(vli.e D(a)r. 1 2t y=;ftrl. AEanori.{Ei Mipr{yBaIIH.n ao3Bonsrorb 3po6rrrr BucI{oBoI{, rqo 1 u .tt(n .Eansa OyHqqin, ocki,rERr ra yMoBoo I . n"r) - cnaaHa OyHKqifl. 3) y = -l(jr). Hexert tr i ,, HaneBarb D(A) i t,> xr rIopiBHs€Mo y(1,) i y(r,t a@ ) - ek ) = - f(r, - (- f@ )) = - flr,) + f(r ) =, ) flr,) > o. Eo y = l(r) - cnaAHa, An" tr< tc2, f@,')> f@"'), s(no e D(A), r,e D(y)r, orrKe, y(x,) > y(x,) rp h> xr'roMy u=-f(r) - spocralo.ra Oyl{Itlri.r. da. y = 11/1 3pocraroqa OyIIKqis. 1 l) y ,ftrr. Hexaiir.. Dgl.x,- DIUILx,.xr 3a yMoBoro y = i(r) Bpocraroira ibyEnqin, ro6ro /(r,) > l(r,). (1) :i{::!i:a.:1i::.iti{a AITEEPA Mep3reK A. r. ra iH. AKaAeMiqHrat piBeHb l:;..i 249 0,6
  • lll Po3r,rsHeMo el'3iilrn ;ltxtt - rlt r,t ztftxtt-ltx rr' 0,603yMoBu (1) fl',) > fG).IIe ossa.ra€, qo y(',) < y(', lplj r, < t, t_ lotrfo g 2llrt - rpo.rarcqa Qytlr(urs. 2ty zltxt.Hpxanrt- DtAt, x2c DIC)r r. x. 3a yMoBoro, = l(') - 3pocraroqa (DyEEqi.', ro6ro fl',) > f(Jrr) (1). Ilopiesr€Mo ptusxqrc aQ.,, ve) s EyneM nns OyElclrii y = -21(t). MaeMo: e(',) a@, = 2f(r) ( 2f(,,tt = 2^!j) + zflx, = 2(f(':,) f(x1)) > o. or,fte, y(,,) > aG) i xt < x,,'t e D(!), n' € D(y)' m6ro v = -21(') e ctraaEoro OyEliqi€Io. 87.s=Inr+ 6-20rt s = x(zm 20) + 6 (*). ,4n.a roro, qo6 dpyHnqi.a (') 6yna spocraloqon, noBIrHIra BtKoEyBarlrcn BIrMora 7n 20>O.tn>zO: n>29. HaiiMesne qine 3lia'reslt.': n'3. IIpan=3 7 OyHllqi.n, = Imt + 6 - 20, € spocraloqorc' 88.!=h' 2k + 3 + 6') A = x(h + 6, - 2k + 3 (*). Ann roro, qo6 {byHriai! (*) 6yna cna{Horo, roBuEHa Birl{oHyBar'ics BlrMora k + 6 < 0; * < 6. Or;ne, npl':&€ (--; 6)OylrKqifly=kt 2&+ 3 +6recnaaHolo = *= Z oy',.qin y = 3,'z b' + 1 trapa6o.Ilr EarpnMneEi Bropy. se" r; n';1={:35=o j[l*rt= . 12x + 48 12tx + 4 12 2) Ilx)=-=-=-,.ir' + 4.x jr(r + 4) .f,ltrqo r r 4i.r.*0; D(' = ( -; 4) .r ( 4; o) u (0; +*)- Ipa&iftoM € rinep6ona, (sir&Er srioi 1re Micrfr6 roqiiy ( 4; 3). I t' 3t-+4l llrl= r+1 (.{+1Xx-4) r +1 r+ 1.D(f)=( -; 1),( 1;+-). rpaoikoM € npsMa y = r. 4, nlta Fe MicrnrE ro.rl(r' ( r; 5). 5) u (5; +*). .-r'*-r--.111 i:.:':i1:j-{l :!ii:-:ii$i iln:::::.fl| l:::::::].:ft|e rp.t v 5) 89.V=3x' bt+t,x e [3; +*). SHanAeMo t. 3pocrae ra rpoMiniliy [t"; +-), 60 (BirKn ro*u 4<a. asra.'6 Or]{(e, rpr D e ( -; 181OynKIIis y = 3ir' D, + 1 rpocrs€ sa npoMitnlly [3; +-). bb IpaoixoM OyHKqii o== Ma, sl{a reperr.rEa€ Bicb Or (-5; 0), a Bicb Oy y ro.rqi (0i npoxon y ro.rqi (5; 10). 3) l(x) = ::- = 1, flr'nJox+4,r*-4. fpaoilioM dpysnqil € npsMa, nlia na- panenbHa oci Or i He Micrr]rb roqoll ( 4; 1) i (4; 1). D(f) = ( -i 4) r ( 4i 4) u (4t +*). 90.a=tu-4x', a€[ 1; +-). SEaiAeMo ' 2 (-4 8 (DyExrris y = b]. 4x'zctra,qa€ Ea rpoMit*ry [t"; +-), 60 lBirr$rr napa6onE sarp.sM- neHi uEE3. ToMv l. -r. a = g. "8 Or*{p, trpr b € (-*; 8l OyHRqin y = rir 4jr'?cna,qae Ha npoMi}Itftv [-1; +*). 91.y=-0.6r lSir c (*). Brxoaqqr s roro, rqo a = 0,6 < 0, ro <Birnltt rapa6orlr HarptMneEi Blrus i Hai- 6in6-e ruaqeHan O) Hxuin r+) aocrrd. npu .r. 3 - . + - ^'" ,r. 2a 2 ( 0,6 0,6 3a yMoDoro BHaqeEns OyIIXqii (*) B rrin roqlii AopiBErc€ 2, roMy 2 = 0,6r' + 18ir + c' a6o 2 = -0,6 . 225 + 18 15+c;c= 133. 92.s=2r' 12r'+c(*). IpaOiRoM Oyn(qii (*) e napa6o,la, iBirnl{' sKoi EatrpsMnelri Bropv, roMv EaiiMeH- -12 nre rHaqe{Ht ut O) HHujfl np{iva. B ro,rui ," 2 2 - " 3a yMoBoro EanMernne sEaqeEEn OyElrqil (*) aopiBEroe ( 3), roMy-3=2.9 12 3+c;c= 3 18+36=15. 25o l* ATTEEPA MeFTKa. r. ra iH, AKaaeMi.{H}ri piBeHb Lil;iili:i:;::::i 2x'1+5x+2 a'z+4x bl ll.r) = -_--=- - = 2(x + 2')(x + O,5l _ x(r + 4 x+2 fiErr{or*0,r* 2; 2x, + 5x + 2 = Oi D = 25 - 16 = 9: ,="3-2.,=!a3=6.5,'4',4 D(f, = ( *t 2) u ( 2; 0) u (0; +*). fpaoiftoM Aarioi Oystr4ii € ripsMa y = r 3, flria Ee MicrlrrB ro.rok ( 2; 5) i (0; 3). D(f) = ( *; D(f) = ( -i 4)r( 4i ::al:i:i:::::{::::* ATTEEPA Mep3rcKA. r. ra iH. AKaaeMi,{Hr4n piBeHb ::::i: 251
  • 'l 6) l{r)=- D(l) = ( -; 2) u (2; +*). IpaoixoM .aaHoi OyExqii e rapa6ona y = .t: + 2r. + :1, sepuuHa snoi 3HaxoAr.rrbcrr B roqqi (-l; 3), a (Bir- (r' rranpsM,'reni Bropy. Ilapa6o,la r{e Micrrrrb ro.rlln (2; t2). 95- 1r f(jrr =,;. i € t-2r +ar. Hexa; r, i x, Eanexarb rpoMix{fty (-2; +-),,!.. > r.. tx) It,.) 4 4 A:L:]-jyL 2t 4t)t 2-x 2t- .t .2 x..Z |x, . 2x._2t lxt_2|)r A - 4(x. r.t rr, 2rr 2it0 60'r -r', 0 r'' 2 0 r'-2 0' or,lte, l(.rr) > fo) p4 i ', Hanex(ar! npoMixKy ( 2; --), ro6ro I l,*r= ,,, c .rr3nHorc qbvjrKui.'o rra asHoMy npoMi,+(Ky. 2) fG)=-r. 8'+ 10, i€ (--; al. Hexan _rr -.r,, h,l , k,i r.,, € (_@; .11 .r - I --: 41. Ilxtt fix t. -ni S.r ' t0 - { x- 6,r, tO, - - .,', ,.8r., +.r0+.ri + 8Jr- - ro= 'i:xi * e1"" *,y = 1',. -,,1(r, + r, + 8) > 0, rooro /tr,) ltr,t. Orxe, /(r) = r, - 8r + 10 - craAHa OyH&qir, F&u{o r € (_-; 4). gz. f(x)=G. ,(D = t0; +-)- Hexan xt e Dlf, r" e DU) i r: , x,, roai tG,) - fl') = .,! - !'t < 0. MaeMo /(.r,) < /(r,). Orxe, l(;r) = yG Bpocrae, snuro, € [0; +-). 98. r)9=f(r), r€ R. 3a yMo3oro y = l(r) - 3pocrarcqa OyHI{qis, f(r) > O Epu r e re. BBiacv npu ,, > ,,Ma€Mo l(r,) > l{r,), ae r, € R i .x, € .q. gEanaeMo l,(r,) f(;r") i noptnraevo": uy- neM..f{ir,} - llr,) = rfl}tr - ft.xz[tf(rt + fljr")) < 0, roaro f(r,)-< /:(,,), rovy y = f.(!) - 3pocrRe Ha MHolRxHi R. -t,, , = lrrr, .r c R. OcKirlxx fixl .O. A |txl Jpocrao,ra SyHKuir. o f(x,) > f(r), sxu{o rj € .R, 12e R, ,-2> rct.IIopiBHr€Mo 3 HyneM pi3xHqro: I 1 Ix,)-lx.) ^ , 1 tr,,t i,,t=-i',tr'. <u roolo v /(t "n*u'HaMHoxHHiR t) s=.rti@, r€ R. ocIltnLRE f(t) > oi s = l(.r) - spocraroqa OyHkqin, ao t(:(tl > Ilxtl npn .r, - r| Ae rr e R, r, e R. IlopirnseMo e ry.nelr pta"s,r-, ,,!lr'.r .,ln'"t. o. 1o6.to u - ,,f;Gr .po"'u, Ha MHoxrrHj n. 99. 1) Oclcinllcu V = f(x) Ha MHoxnEi rR € rpocraroqorc ii npr qLoMy /(:r) < 0. ro npr ). r, Lrj € R) flr,l < l(jrr). AaEo rbyHxrrirc, = f(,).-BHaiiAeMo: l'txtt f'lx,J = (fG t ftx,lftrt + l(',)) > 0, ro6ro /:(rr) > f(rr,) trpn ,r < ,,. 01)t(e. y = /itrt ue cnalHa OyHnuir. I 2l g = lD ). ,r € R. BiAoMo, rqo /rnl < 0, OysRr{ifl V = l(.r) 3pocraloqa {DyHx- qis Ha Mllo,rlulri R, ro6ro anr ,rr € R i jr, > .!, BlrioHy€rLcs piBHicrb /(x,) > l(-r,). nopiBHrro J lrynFM pi.rn"u,o, -r .. I llt') 1",' -o-,no,n J ,-1Ir. Iktl /{jr,l/tx.r - ltx.t l.t,t lx 2r! + 2x + 4t' .-=r-+zx+4. t-2 s4-tr,r,r= r +4n+4_I1 != r +2 r - l _ (jr +-2)i (' - 1X' + 1) t+2 ir 1 x+2-(x+ 1)=n+2 r. 1=1, D( =( *; 2)u( 2j 1) u (1; +-). fpaoixoM aaHoi $yEklrii e npaMa y = 1, gl{a He Micrnr}, ro.rox (-2j 1) i (1; 1). 2r: - rt r:tz - rt2t I(I)=-= =!2-')=2r- r', D(n = ( *t 0) v (0; +-). fpaibiEoM aaEoi rDyHXrrii e napa6ona V = x2 + he, BeprxuHoro rrcoi e ,ro'rKa (1; 1), a *airxq" HanptM-,lesi BH 3,60 a = -l < 0. lpaoili se Micrtrr! To.rKr (0;0). 6ir 18 6lx - 31 6 3l u= -= = r+U." x'3r x(x 3) x ' * 3. '(' = (-*; 0) u (0; 3) u (3; +*). lpaoinoM Aanoi iby'rKqii e .inep6o- ,ra, {uirirr' flRoi He Micr.srb ro.rKu (3.2. .. -r' + 4r: 5 -(irl 1)(,r': r 5) .*' 4'= "rr = t* 1x*+t, = =12+5,r.*-1,x+I. D(a) = *: -1) u (-1; l) u (1i +*). fpaoil.oM AaHoi dlyExqii € napa6ona, B€prxxHoro sKoi € roqKa (0; 5), iBirK," tranpsMneEi Bropy, 60 a = 1 > 0. rpaoiK lre Micrurb ro'roK (-1; 6) i (1; 6). l I or*e, anr x. < jr. Ma€rro I r I -.*' " fijr,t lr,) 100.y = l(r.) + s(:tl, r e M. OcRirEKu Oyrl(qii l(r) i c(,.) - apocra,o.' ua MEox,rHi ,,u, ro an, 6ya6-flrnx ,. E M 3a yMoB! x" > r,, BrxoHyerbcs lnMora ir.r > lxj ), g{jr-) gtj,l. nopiBHgeMo 3 HyreM ;:;::-:*i::.::t:::i:;: A,lTEEPA Mep3lek A. f. .ra iH. AKaAeMieHri piBeHb ::i::t 253 1 roMy y=- - qe cnaA{a OyuftrriE. 252 :::::: AIrEEPA Mep3rsK A. f. ra iH, AxaAeMi,{Hnn pigerr i:i::.:li:$iii:i:i:::i
  • pi3Exqlo: a(j.,) s(x,) = /(',) r c(r',) flr,j,) - c(j.,) = (flr'') ('x)) + (s('r) c(jr:)<0' ,ou,olr,,r ttjr r. or)v".ir " 'rr't v''r i t' x' tt i U ovv'l'v 'ui' , /rr) atr) ,rjo' rr, '' Yro rn tZ II c ttocitt i" ",*.'.'. d,vsxqi; /(n) i e(x) 3poc"'nr. F' MHoxnHi M flKUro t' > i''' ro ftr | > ftx t i El:r^t ' llx.) AoAaloTti ro'rnelrHo ocratrHi tsepiBrrocri' oaepxvcMo ii':i r J,'1, ii',r rt' , or*{e' cvMa rbv''lqin l(.t) i s(r') e 3pocraloqoto ovrx' ui, ro rra 'rloxlrri V 1Ol. Hj. Hanprr{,14r. atsuro 'i'}rrK t st't 2! I!t -! -p''': "'" l" ]ll'' ' [0; +-), ro-ri vfiuris v(j.) = ft') - e(ir) = r] 2jrr = r'tcniaHoroQvH1{ur€rolrirMFo x'rtsi [0; +-). 1o2.Hexan.i.r € M i r., e NI, x,> x, roai l{r') -: l(jr,)' c('') < s(:'r)' 5() d'jvHkuii ' - g ili"i i y = ct,l ciaa}Ii na;Ilo,1!trrli 'vr' ea vMoaoio 1ir; -' o' eG) < 0 no8eac i'., ''.,. ,f,u""uj" y = /(') s(') e spocraroqoF Ha MEo)litrHi M' Po3r']IflEcl1o pr3E' ,,- ,r, r'l ,r""r= tr.,) c(r,) l(j.,) s(.t,) .:0, ro6ro v(x,) '' l/('r) or'{e' r, > r, :r-,;; ,,i r.'."vri r''' s{'' rpo" rrovoumter{u 'oH'Hor'Hr '1I 103. Hanpntraa: OvHRqin ir(jr) = xtr(r' 2) lle € 3poc Ilcxari /(r) = '': i s(r) = x 2 spocraloqi OvE1rqii '{aMH(,itrHi[0; r*), a-re q]vHRiris,(:n) = j"! 2)-rt 2t HP. 3pocrdn,orrl ", Mho)H/ii l0: -l' I ll.nDU{ir{{tsvI0; - 14J""' iai'(rlc nad' aH1 lDo- _3 Mirl{k,Iai]F)3pocta€ lO4. cyv" nBox qr'.c r aopiBF o' 8.HFbnrcpurei rn-oo / rD)rc ". ' 1) Poamsserro rlvrlnqirc v= a(8 a), s=80 a rprtbiRoM ' nar'rbor'r' ?Rr1r" -8 'koi HanDq{,lPHr ^ ' l ()610 ' ' 32 16 ' 16 uP H'nb rr'' c r a,reH.rfl,IyHtsuii !/ at9 dt tf{I 'o n'pde "/'1o '1 ii lpvrP 'H'no l ro noojror qlrx qrcen € Han6inEurM, re 'rtrcro I6- 2) Po3r,lflEeMo drvlrrirrilo v = a: + (8 - a)i, v = a'+64 76a+a'1=2A' 16.,+64- fpa 16 tlilioM qi€i 4 vtsllqi; e napa6ora, (!ir(u"l{oi EarpEMjlesi Bropv' a x' = : = 4' y,=2 16-16 4+64= 32+64=32' qlrc'{o32 e HaiiMeH Irlt 3HaqeHIt'M cvMl' riBaApariB 3aaallnx qIrcer. 1O5. P --. 200 ' B ztci ABt 20o AD AB 100. h'x"t AD :(' rcn ,r,a = IOO ,. 'S,,,",,='(10o .I)=100:r a! Po3tnflEeMoOvH- nqiro ri = 100r Il rpaoi(oM e rapa6o'1a' (Bir(s' Enoi Ea 100 npFv rF dH/J. * '1" ro u 50nu 2500 2i00 A BnpaBu.qng noBropeHHg 107. 1)(7):.7s =7t.7'=7.= h. 21 36-'6 6-6'0,,c ti. 36: ", ur:.:;," = (25')' 5' "1 " i " r " 5 r25; 2) 0: (-3,7)3; 5)( r7f= 176; 3)(-12)'<( 6)a; 6) (-34)r :- ( -39f. qt'c'Io 2500 € naii6i'1!ue 3IIaqerIIr€ OvH(qii v = 100ir - ir:' roMv Eaii6i'1!Il]a ltroultr Aiffrllrlr aopiBEllr€ 2500 M'. 106. AaHo f(x) = 1:, r. e R. Hexan r., € (--; 01, x, e t0: +-)' roai r,:-'rc' ftqo ,x'l ': r" rogi ""'i O)' sErqo lr.;l > tr,l, ro,ri :ri < 'i (2) vMobf (1r i {2r^arctt -:lllal:T Jro6rr L!'' ' oBoK. Llu /i') r H' ' H Jpo'aao 'oro i " 'JHo'' Ir'' 254 i:i:: AIfEEPA Mep3flcK A. f. ra iH. AKaaeMi'{H n pieenu :i:i:i:iijl::ii:i:::::i 41 0. 125 32i rro.srJl 12 r 0.; 2'o 0.5 .2 l .: 0.b. 0,5 0,5 ' 0,5 2 1o8. 1) 18a3 = tt I l' = 18 + =;; t,t" 2) r18a):= 18 : =( 3)r=9i ail 3) 16 + bf= 16 + ( 2f= 76+ 4=20; 4) (16 + b)l=(16 2)'=141 =196. 109.3ayMoBoFa > 0, b> 0, ro/Ii ai + b3 (a'b + ub') = u3 a'b+ b3 -a.b'.= = a!(a b + bb - a)= a,(a _ b) - b,(a, b=(a- bxa, - br= = (a b)la b)la t b) = (a b)'(a t b). Bnpa3 (o ,)r(o+t) >0, ocd,'r!l{na'0, b > 0,,tor{y ar + b'>a'b+ ab' npa s'r6!a epiBrriclr,. l10. 1) ( 5,8)': -- 0i 4) -8$ < (-8)3; 2. napHi i HenapHi OyHKqii 1 1 1. 1) y = l(ir) e rapHoro OyHriui€rc, ro6ro fl- jl:) = i(r). fll{qo f(7) = 16, ro i l( 7) = 16. 2) , = l(r) e EenapHoro OyHlirii€ro, ro6ro lC x) = -l(r). flnrqo /(7) = -16, ro fl-I) = 16. 112. y = l(r') € rapEoir, ro6ro /( r)=flr),ronii 1) f(2') - f(-2 = f(2 l(2) = 0, roMy piBFicrB f(2) f( 2) = 1 Henpar nbHa. 2) piBHicrr, l(5) l( 5) = 2 llerpaBr.,rblIa, 3tsa.Iel{Fn l(5) = l(-5), 6i) rDyHX4n napHr. ro!) ro6l-ox ' 'rrri " a"arr e. a | /l l) /' ' ' ,. ,,*, ,:,-:"." /r | | 0 !. no.'-r. 6Ha. /r Ir /(l) l t) I 13. y = l(Jr) € naplloro dryH'{[iep, ro6ro l( x) = l('I). PiBFicr! j]ll = 1 u,,*o,,y.'*o, /( 1) 5()/( 1)=t(1),rllqo t€Dl i1er(f)il( 1) * 0 i /(r) I 0. Anc, rnrqo 1e,(/) r I s ,U). ro rhs r* " ' p'""'""' /rl) I F Rr{oHy.rq, r. t( 1) 114. y = /(.') € senapEolo (DyER4i€ro, rosro l( r) = fir). 1) l(1) r l(-1) = l(1) l(1) = 0, roMy piBHicrB l(1) 1 /( 1) = 1 EenpaBxnBEa. z, I'.-:' !:' r. ','uro ^ 2) . 0 i /(2, , 0,ovy p'BH'*" /1 ]) o HF,.ph t(2) /c) t(2) I 15. 1) J. E [ 9; S]. Mnor{rEa cr}ierptr'{Ha BiAHocno llynr, roAi rbyHlrrtis y = r': e rap soro, 60 a,tE Ro}]txoro r, icnye npormre)I{lre rioMy ( r,) i (x,): = ( r )1, robro flx) = fl jr). 2) .r G ( -; 3) L, (3; +-). A,r'r xor{Horo € ( -i 3) BaBJ{qr Mo}r{ Ea Bsanrfi liAnoBiAHe nporxrrexHe qr'rcro ( jr,). MHor{xEi (3i ]-), i (r,)'!= ( r.,)':, ao6ao ^r) = fl r), roMy, =j.'j- rapHa {byH(rris. i:::::::::i::itiii:: AnTEEPA MepsncK A. r. ra iH. AKaaeMi..rHun piBeHb ii:;t 255
  • 3)x€[6; 6). 'DvHKrris, = " He Mo'{ce 6vrT napEoro' 6c annr= -6 IIe Mo'i{Ha BEaiirr{ nporlrne)+rHe qrcrro 6, an}ile 6 4 [-6; 6). a) :r e 1 -; 41. ovHKqifl v = a'?Ire Mo]l{e 6vru flapHoro' 6(] Ar's .I < -4 se Molt{Ea snafiru rporlrner+{Iri 3Ea'reEHs. MHo}trUIIa ( -; 4l ae € crMerps.I}ioo 116. 1) f(f,) = 171. fpaon{oM QvHriqii € rpsMa' sHa rapanenlEa oci or i-rpo](oa'rrL '"f"" i"""v t,; lfil, 'o'v lt ,l = tzr. orxte' l(:,:) = fl-')' roMv l(x) = 171 rap il it,l= s,^,te R:f( x= 5 ( ')1 = 5'{- l(r) or,re, l('J=-5'1 e napHol(, OyHlrrrielo Ha crMerpnqnil; MHoniEHi (-*; +-) eiaHocEo roqnr O' i -L l-r.l l /:_l r' I 3r /rrr ''--i. ,,',= i ,i -; : =rrjr) or'j{e /(r) r'-a 'ndpts.ro rlyerqierc'ira ctruerps.rHii MI'oxsIIi ( *i -21o (-2i 2) u (2; +-)' q f@= E- + Ja+ x, o6racr6 BIr3Ha'reHHs Ovrrrrlrii [ 4; 4]' i a= rZ;. uZ- = 'it'- ' *,tri = ttrl orxe' itrt = 'f+-i+''[+ r " "tp"". OV""oi". "a crMerpxqsili MnoninEi [-4; 4] BiasocHo roq(lt 0' it /rrr" --L- , o6nacrb BxJrro'{PHHs O!HKui-,: I l: ll: Jl-.r .,/x+1 t-Jt /{ ',r ,i,;-F=-r,r.* ,r*l) "[*-'r'* Or*{e, cpyllxrria f)d = -: t:=- e naprolo Ea c'MerpnqEiii Msoxxrli [-1i t I 'l-t x' I uiaEocEo roqr$r 0. 6r nrr . rx , 2tx 4 lr 2,l' t 4, o6narrb Brs"aqeHHs Ovlt(uii: { -: -): 7-,, ,-t zr-, 4 -l x-2) r 4! -lr 2t) -4 t tx 2tx a - ftx' tehoto.,qo a = d. roM) x-4t x 4"! 4tx'4t drxe, l(r) e napriolo iDvllKlrito sa clrMerp{'rHifi MHo'lrclxi ( -; +-) BiasocHo roc' xr 0. 117. 1) l(:r) = r", n € N, n - napse, jr € R. fl-ir) = (-r)" jr' - l('), l(') e naptlolo OvEnqi€Io sa cl'Merpsqsifi Mllo]*inHi (-*i +*) BiAEocHo rorKr,l 0. 2tflx)= 3x"+ ir 1,r€R ^x).4lxf - x-r 3r.? 'r-l'lrl' b;;'., ;" 4 = i ,- o'*", i(.r) e napsorc ibvgllqieto Ea c'IMetpn'rgiii M:roaaqi (--i +-) BiaEocEo rovtiu 0. el ifrt =.,,f,' 3"+5*G'*s"*5' xe R(x' 3r+ 5 > 0 i r2 + 3' + 5 > 0 npJ' jr € R). fCtl' =,F*l z, t n. v[,)' * s(') * 5 = !t' . 3t. 5 + uE - z' + s = fO' Oi*", ftrl - Eapna OvHnqis Ha crMerp"q{iii Muo'{lisi (-*; +*) BianocEo roq Irfl 0. a) l(') = 6 - '' r n-,,;1 = uG 1-'Y = 1G:? = 1,;. or,iie, l(jr) - napHa Syt{Ktlis rla c"MerprqEin MHoJ'iI'Ei (-*; - '6)" (.'6; * *)' 5a-2+l;x+2l 5r /ur -:' ;= 1 j. x I -1. x t Ll . 5r xr-2'r15 Ixr-2- si 2 F-5jr-2r =5':]:j! l. h,ln-xl - i),.1 - x,_1 r r Or,{e, l(') rapHa ibysliqis Ha c MerpE IHin Mso]*iEsi (--; -1) !) (1; +-) 256 i:i:i: runrgspa Mep3ncK A. f. ra iH' AKaaeMi'{H}ri piBeHb ::::::: :::::::: :::: ::::::: or tur --L-- - l - I .=- 1 {3r ll' t3"r-lt l-3.r Ir ( 3r' Ir' .(3.r-t) -(3x lj- = 1- * --L- = r,,,.(3x + 1)' (3x 1)' Orxe, flr) - napHa Oyrnqis sa Mso,(r{Hi clMerpuvHiri BiAHocno roqKr.r 0. 118. 1) l(r) = 4r:i, o6nacrE BrssaqesEs: xe Rif(-rc-4.( r1 = 4x1 = -f(:(). Or,{e, l(r) € Henapsolir QyHI{qi€Io Ea Mso'{aHi (-€; +@), crMerpuqHiri BiaHocHo 2) fla)=2x 3r3,re Rif( r)=2.(-r)-3 ( r)E = 2r.+3f = (2t - 3x5)= -f(xj. Orxe, flr) e nelapHorc ibysliqi€Io Ha Mnonirlri ( *; +-), crMerpurrHiri liAHocr]o ro,llrr 0. 3J fe) = xx), r. € nj l( r) = (-')l-'l = rr.l = l(ir). Orr{e, flr) e HalrapBolo Oyllnrri€Io l1a MHor{rlri ( @; +€), cEMerprr{Hiii BlAHocHo 4l f(') = (5 r.)5 (5 +')' = (5 - ('))" (5 + (,))' = (5 + r)5 - (5 - x)5 = = ((5 r)' (5 + r)'?) = -l(r). Or,rc, l(t) € HenapHoro OyH(rdeb Ha MHor{trEi ( @; +@), cxMerprqlliii BirirocEo 5) sQO = E a ,tT-n, ct-i=J, e,) J,+t xt=rZ;-rZ:; =,( ,E*r*"E-)= it,l. Orr{e, g(}) € EenapHoro OyEEaiero Ha MHolrrsi [ 2; 2], ctlMerpn.rfliri siAfiocEo - 3x+2 31 2 bl g(r)=-+-. x' x+1 x'+r+1 3.x t2 3, 2 3"r-2 3x12 /( r',' x'ztttl t "r'l .r'-x t-l l'?x 1 ( z* z 3r+2 = lrL+1+,-.4r]=-/rjr) g(J.) a seflapsoro OyFriqiero Ha MHonirHi ( -; +-), crMerprqEin RiAriocHo ro.r nr 0. re. rr /(-Yr ' 1.t,,, ' j= ,..1-t n', Ou{e, l(ir) c retrapEoro OyFnqi€rc lra MHorirHi ( -; 0) u (0; +-). 2) ftx)=(r"+ x)(x' r,),xe R; f(-'=l( r.f +( i'D(( j'), ( r.f) = = ( :.3 xt(x1 jr') = ('. + rxrl - r') = -l(r.). Or}rra, flr) e l]enapEoe) OyFruri€rc Ha cnMerpuqHjn Mnollxsi ( *; +F) BiaHoc'ro 3) e(j')=r",r€ N, n llerapHe,.ir € -R; c( r)=( r)" = x.= f(r. orxe, s(r) € HenapHoro oyHrirriero Ha cr.rMerpqqFi; MHo,nrHi (--; +-) Bi{rocflo t,-"4) 8(r.)='" , .r , 0; g{ jr) ' , g('t. Or,Ile, €i(r) € HenapEoro OyH(rri€ro Ha crMerpFHin MHo,{rEi (--; 0) u (0; +-). ;) c(i) r' .r - (-3: 3r; ,/3 r J3+r r rl4( ,l sljl. i3 J 13 r (J3 r 3 l Ji r ./3'x :r;::iiliiiiiiir: AITEEPA Mep3reKA. f. ra iH. AKaAeMiqHr4i piBeHh ii::: 257 [--,-;)"1 l,l..,l;,.r, : r.. i.-.--.-..-.. ::til].ai:L.:.!: :i.: !!:.iill: 'i:+i:ii'lii
  • Orx{e, g(r) e EeflapHoro ibyH&rliem IIa crMerpuqtiii MEo)r IHi ( 3; 3) BiAEocEo . l-4,x t.-4..,.t ax r ax-rl _ lqr t.qx t .ptxt. sqx)= -. :- (,r, -r r I r' I OrrKe, g(t) € Hetraplrorc Oylrnqi€Io Ea cv MerprqHii MHot{rlrni ( €; -1) r (-1; 1) u (1; +*). 120,1) f(r = !. O6nacr6 Blr3Ea'rellns OvHRirii: (-*; 0) u (0; +-) IIn MHo'{rEa c!r- MerprqEa BiAHocHo lryn.s. sEaiaeMo f ( 4 = ==:= f @)- orxe, SvEt{qis l(') x-l -2l f@ = =. o6racrb BnstsaqenHn OvEltlrii: (--i 1) u (1; +-). Us Ml{oxrlrEa se ruowe oyru cr:oaerpllqnorc BiArlocllo roqxlr 0, roMv OvII&qis l(t) se Motr'e 6vru sEi llapHorc, arli IIerlaplrolo. 3r frxr = *. o6nacrL BruHa.r€IIEs: (-*; 1) u (-1; 1) u (1; +-). LIn M$or{r'Ea I t-rrr I r' 1 cvMerprq'a BiAEocEo roq*r o. 3'aiiaeMo tr-"r = arffi =,, r- = flrr' or,'ie, OylIlcrris l(t) trapsa. 4) fG)=Jr"-1. o6nacrb BrclracelrHs OvHKqii: ( -;-1)u(1j+*) IIg ruHo:nnsa c'Merpuqga Birrlocllo ro.rxlr 0. sraiiaeMo rcn = 'l.,r" L = 'lV= = l(') orxe, l(r) - rapEa OyH(IIis. 5) l(r) = .rt L .,6 + 1. O6nacrE B[sHaqeHHe OvHRaii: [1; +-r' ris vuoxrua se € cnMerpr.rqHolo BiAHocIro ro-rKr 0, roMv Aasa OyH&qis He Mo*ce 6yrl'r alli trapEoro' aHi HcoapHoro. 6) /(x) ^ , :. Oe,ra"rr Bu3HaqeHHt Sytsxuii: x3-rro,ro6ro( -;-1)!( 1;0)u(0; 1)u(1i +-). . x -x tx'-t") x -x 3.ranaeMo /( x)=- , = lx- - t) (Dyl{}{rtin /(ir) Ee € asi napHoro, asi HerapHom. 121.1 f(', - x'+ 2r - 4, x E Ri f(:t) = (-r','+ 2 (-r') qir /(x) He c aBi napHoto. aui HcnapHoro Ha crvarplsHifi 2t ttxt 9, ., orn t--; 3) t-ar a). {3: -):' I, -9 6 l-rl'3 613 f( x=-:- 1=-=-Ilx). ( x)'-s .r" s lt ll .'- =--L-=-/(r,. O,HKqia l(r) c HenapHoo I x'J" - 2 l-x) -x" - 2x x" 2.' Ha crMerpuqEiii Mrioxc""r (--; - "E) , (-"8; 'E) , (.8; + *) BiaEocFo Eynn. st ft', = !l!7. o6nacrb BusHa,{esHs OyHr{qii x + -{r, ro6ro MEo,rinHa (-*; -r') u'' 2t+12 lJ ( 6; +-) He € cnMerprrrHom BiAEocHo synn, 60 qi,Icno 6 He Ma€ rporlrne)rGoro ( 6). roMy naxa OyHKrr'fl HF. aHi napHoto, aHr BenaD-oro. of(t)-1x - 1l -2lrl +lr+1, jr€ Rtf( t)= x 1 2l'+ r+1= =lr'+1 2l.!i + r-tl=flx). Bieor.ro, urol r 1=):+1, '+1=r 11. oyrllcrri.a l(r) € napEoro Ha crMerpn.rHin MHoi{ir.'Hi ( *; +-) BinHocllo Hyrrs. 122, a) IapHa OyHXqis; 6) EerapEa OyH(Iti.s; l;: .:,a:{.i$: li:ii-l:di:i: li ':ji::-::.:::U vitlii'.ii:iil li:l)::::*l:J i :;;:::::::::i::i! OyHKqis l(r) e HenapEorc Ha crMerpFrEiii Mllo]IctrHi (--i 3) .r (-3; B) DapEa OyHKqin; :ai;:ilitllllil anrE6PA Mep3rrK A. 9+ r) Eeraplra ibylrxqis. 123.1) A = f@) napEa Oyllxrris, r € [-5; 5]. 4=x'-2x-4.Oyrrlc- Mno,ntrEi ( -; +*) Bia- 3) u (3; +-) I I /r-.r) l- I =lttt.3r /rxr=l r- -. xrl,xz I l-r. r-.r @yH$qis l(r) e rapHoro na MEo,riIrHi, € ( -; 1) u ( 1; 1) u (1; +-)' q Ixt- ,I ^-. o,fl (*: JzJu(''lz, Jzl -,(Jz, --), v'-2x 258 ll{: AITEEPA Mep3reK A. r. ra iH. aKaaeMiqHrar pisenr liiiiiilll::ii:.i y = f(x) senapEa Oynxrrir, f. ra iH. AKaAeMi,rHran piBeHb li.1 259
  • 124, I'J 2) 125.f(r="-4awvr>o. 1) l(') - rapEa; 127. /(r) - Eerapsa OyEnqiF, 0 € l(f), rouv l(0) = 0. 12A. ft!) Heuapua S! Hxuis. BoHa nae 4 Hyti. AoBeaeMo, nro 0 e D(r. flpmrycrxMo, ro 0 e D(n, roAi l(0) = 0' ro6ro OvHXqin Bnie Ma€ 5 HyniB, s aa yMoBoro - 4. MaeMo npornpiqqs. Ort*e' 0-€ ,(r. 129. Ix) - HenapHa oyHKtrifl i Ma€ 7 Hy'rie. ,(f) € crMerpnqEa Msox{LIHa BiAsoctro ro'rKIt 0, lra sxiii Br3sa'resa OvHKqin l(t)' l(0) = 0. 13O. flx) - napEa.byHKqin i Mae 7 sy"ris, to,ci f(0) = 0, 60 D(D € crMerp"qna MIIo- ,rinEa BiAHocHo oci Oy, Aa Eftii Blr3Hs.resa abyHRqis l(t). 131. 3a yMoBor M orMerplrqHa MAo*{ssa Bi,qEoeHo toqarKv RoopAl-rlrar (o6nacrb BEBHe.rel{Hs OyF&qii r, e@) = f(x + r), roAi g( ir) = l(-r) + l(r) = s(x), ro6ro EG) rapEa OyHHuifl, 3a ylaosoo M - cnuerprqlra MHou{ItEs BiAEocno Iloqar&y l(oopAr'Illar (ofulacrb Br3- rla'reEEs Oygxrrii n, h@) = fixl - f(-t, roai ,(-x) = l(-;r) tQ, = -( t) f(-x' ro6ro t( ') = -t(t). oril(e, n(r) - HenapEa lbysKqin 132.3awoBoo I ig trapHi lbyEnqis lla MHoE{I'IEi M, ro6ro l(-t) = f(') is(-t)= g(a). florpi6Ho aocniarrr tra napHi.rb SyHHqiIo: l v = f@) + s(t, aC t) = l(') + €(-t) = l(ir) + s(n, = 9(r). ovnKl{in I = ftx I + e(x, - [apHa. 2 s=f(x)- sXt),v( r)- -x)-c, t)= x) -s(t)=y(a). (D]'El{qiss= x)-sx- rIapEa. 260 iJi AnTEEPA Mep3reK A, r. ra iH. axaAeMiqHnr piaexu ill{liiNi'i:li;I :t s = f(x . s(x., a(r) = f( , . c( t, = tG. . e!c) = y(t). @yllllqis U = /(r) s({) - r33. AaHo /(r) i €(r), BllsEa.reHi Ea Mlro'r(trEi M, f(itJ - napEa, ro6ro l(') - l( '),a g(r) - neDapEa, ro6ro g(-r) = g(r). Iorpi6Ho AocniAr.rr IIa napHicrb ibynKrrilo: t) a=f@)+ e@), a|x,= f(-z) + s( x= f(xl - s('). @Frrcqis y = l(') €(r) re e aHi trapHoro, aIIi serapEoro. 2J a=f@) e@,v(,)-fl a) s(-:t= fG) +s(r). @yE&qisJ=l(,r+ s(r') se , asi EapBolo, aHi Henapsolo. 3)a=^x) cG, ae, = f( ', e(t)= r. ( s('D=-^r).s(r)- y(,). oyHKr{is r, = l(r). g(r) € HetrapHoro. 134.@tErcaiifigB 3saqeEi Ea MHonirHi n4, /ig - ueDapEi OyHrqii, rc6ro l(-r) = -/(r) ig(-r) = g(jr). Iorpi6Ho aocriarrn sa napEicrb OyEftrrilo: 1) a=f@)+ st, vtr., = f(-,) + e( r)=-flx)- c@) = (l(r) +s(,))= y(r). @ysriqis y = l(r) + g(r) - lretraptra. 2) a=f@) s(rr, y(-x. = fl-x) c( Jd)=-l(r)+s(')= (flju) €(r)) = -y(r). @yE- Kais a = flx €(r) - EerapEa. 3t s = f(x). s(x, vttcl = fFr',.c( it)=-flr). (-e@D=f(r). s(r) = y(r)..DyHXrru ,=l(r).s(r)-napEa. 135. / ig - seDapui, ro6ro /(-,rt ftxl, gFxt = g{xt i npr aboMy OyHnurt hIt'l - -- 3safrAeMo ft(-.r). elxt fl-tl fttt ttrtht x) . = -- = . lr-r). oyHKtris ir(.r) e napHoro. gt xt gr.r r g{,r) 136. I i g lbt EKqiI, oAEa B srclrx napna, a Apyra seflapua. <lyrrrrris h(i = 19) flErqo / r'apHa, ro l( a = f(xl, a s - rieraprra, ro g(-x) = s(r), roMv fGt ftrt ftrthFxl. . . et-xl sltl strt flKqo l- s€trapEa, ro fl-r') = f(r), ag- napEa, ros( r) = €i(J.), roMy .. ft xl ftrt 'ftxth( lJ .- = - ' ,(r.). OyHxuir lt-rt HenapHa. c( .r.) c(.r) eG'J 137. @yEX4is / BnBHaqeEa Ha MEonirEi fi. 1) Hanpuftirag: y = a3 - Henapsa Oyl{ftqiF fi Ea MHoxcrHi rg 3pocra€, ocdnr,xr An! t"2> x) (tt e Rl, aG,, - a@) = '3, t > o, rc6rc v@,) > uQ). 2 Hanpve'nlat y = '4x HenapHa OyunEis fi Ha MAorrrBHi R cna{a6. 3) flpulrnaa seBecrr.r He Monitla, 60.anqo ibyHriqis rapEa, ro ii rpaoix c[Merpr.q- ssii BiariocEo oci OV, roMy Ha oAsifi riAMHor{rrHi QyHprqin spocra€, a Ha iHrrii cra- Aa€, i IIaBnaKn (sa yMoBs, qo o6nacrr, Br3naqe[Hs cxMerpr-rqHa MnoxuHa siAHocEo sy.ns). 138. I rapEa OyE&rris, .sna spocra€ sa npoMix{i{y [0; +-), roAi na npoMir{(y ( -; 0] roHa e ctranHoro, 60 rpaoiK O).Hriqii cuMerpr.rEnii BiAEo$ro oci Oy. HaDpuRnani lJ = t2: y = x). 139.1- HetrapEa OyHlrrtis, BlrsHaceHa na MHoxr{Fi R, spocra€ Ha trpoMt(Ry [0; +-). Ipaoix EetrapHoi Oys&qii crMerpraqHrfi Bi{Hocno noqarlly KoopAt Ear, roMy ii Ea xpo, Miliiliy ( -; 0l qs dyEl{qis spocra€. Hanpxknaq: o=L, o'oro t". i:ii:;liilliil:it: AnTEEPA MepsnrK a. r. ra iH. AKaaeMi,{Hrr pieexr :ii!: 261 126, a = f@)= o,sf , r e LOt 2li aQ rapEa; flx)=-:, !>2. 2) g(js) - EerapHa. 2l f@) I{enapHq.
  • 14o.J napHa.byE'iqis. Tlli{.v) 2. TqI /l'rl 5. oc,(iiLHx/- napsa OvHHui', ii rpaoiK cl,verpfiqHri EiasocEo oci 9. rovy ,minrllx) 2. rnsx /(r) = 5. 141. Oyr&qi'I I e senapnoro i nti'll(xl = 1' maxfla) = 3. Oc(inbKr'r f(x) - He- rapEa Oynriqin, ro ii ryaoin clrMerpr'qHri BiAHocHo roqarKv rioopAl{nar! roMy min l(') = -3, maxl(r)= 1. I-i: 2) l-3: -2) BnPaE'l Anc noaropeHHt u 7x 3, l{ 3*?-" (l), 142.1t l" l"-':' " ll 6xs. y s, I.r - 6113 I 7xt-tB 1xt'z=9 tzt. PoaB'rJ*{eMo piBEnl{Hn (2): x2+l8r+4212 g 42x- 4g!'=9; -6t2 24a- 18=0; t'+4t+3=0;''= 3 a6o x = -1. 143.3d )voBoo /, /r sa I ror. 6 xB. I -6^ l.l .oa.: 60 s 66 66 66 66 ll 6 6 I - ^ '=t=t' t=;-' u, ,-', l0i u ,, t0{r) ra lp{ roarHh Bonh opo lxaru 66 HM, ro6ro 3D1 + 3u, = 66; +D,=22(2')i t> 0, I,j >0, u,> 0. =22-D,, 661 = r:l)- 22 D, u, 10 = 0; 60u, - 1320 + 60u" - 22v" + o: = Oi o +98a -1320=0; .D -qg' .lSzo 24ottl32o 3721, J3721 6tl 4 D, = -49 + 61= 12. r,, = -49 6l= 14O- BpaxoBymqr yMoBy ,, > 0, MaeMo u2= 12, ro4l Dt= 22 12 = 10. BidnoqiAb: 10 F"Lr/roa.; 12 r.M/!oA. 3. no6yAoEa rpaoiKiE OyflKqit 3a AonoMororo reoMerpreHnx fo 'o 22, t' 'I'o3B rlKeMo rxcreMy piBHflkb: i6 6_ l. [u, r-', ro ' PGB'.'xeMo piBEnnEs (3): 60tl, 60(?2 p,) p,(22 1,, D,(22 - D,) u" + O, L),+ 22. '.4:i a-.:.t:.:'tt :i:t:.:.:.:i.I. flxrqo jr = -3, ro 3/ = 3 - 21 = 18. ffxqo jr= 1,roy=3 7=-4. Bidnosidb: t B: _18)i I t: -4). l*_q=ro. ,, Jt - u, 2r! too. atx vl - roo. ] ' , ir ar '' ly,, s, u-. Bt l['-r' '0. Bi.)no.)idb: (gi-t): { li 9t. 'fr t Y = 6; lfz* = re. l[* = g. ]lzs = -2. ly = -r, JP'= ,' l['= '' lL2, = 18: [1!/ = e. "r[,tv',0= 15. [x-u-rv 15.H"*u,;, tu=a.rc b. x'zu + xu - 54t ltvk ' u = -54' l, r b = -15. ]d -15. b. rlr It'" 54: lrr l5 bt = -54 (2r. PorB exeMo piBEflHHt l2r: 15b - b, = 54i b' + L'b 54=Ot D = 225 - 4.1. (-541= 223 + 216 = 44li A -ls{ 2l -6 r, a =_15-2I=_!9 t8."t22-"'z22 g$rqobr=3,roa,= 15-3= 18; sRrco b,= 18, roa,= 15+18=3. 1r ]x ' = -ls lx -I8 e (3r po3s sxeMo piBHnsss r4r: lxs 3: L( 18 y)y = 3 (a). ,18v y,=3,a,+18y+3=0; 2=sr-s=zg, y,=-o-.fia; y"= -g+rte, roai '' =-18 (-o-.fa)= s+.,,Fs; ,,=-rs-( s*"8 )= g .,88. orxe, [-o + .,Fa; ,-.,fis), (g '[s;-s*'q8). 2t x + a = 3' [x 3 - s' {51 poc" '*.'o pi""',r' (o), l'y = -rA: l{3 ,)y = 18 {6). 3 t s t2 3u-y"= 8; y" 3y 18=0;r=9 4 {-18)=9+72=81t u.=;=;=61 ," t-n=j 3. rori .r, 3 6=-3..r, 3 {-3) 3 3=6 "22 Orxe, (-3; 9), (6; 3). Biono iob: (-3i 6), (6; 3); (-e+,fi8;-o-'fte), (-o -.,fia; o*.4a). 262 ::::::: AnrEEPA Mep3nek A. f. ra iH. aKaaeMiqHnr pieeHb :ii:::iii:i:::.ii:i::i 145. BiAnosiAb: 4) y = (t 42. 146. BiAnoqiAb: 1) a = f + S. 147, BiAnMiAb: 3 Ea 8 oanHr.rrlb rpaBopyq. nepeTBopeHb 144"AarJoV=t'. 1)a=x'+5; 4Ju=(x+6'; 149. a = fl;r). 1y=f(xr-2; 2a-f@r+4; 3)y=f(r-3ri 4a=fk+1; 5) a = -fl''); 6)a=3 f(r). 2)v=Q a)'i 5)y=(.Y-g):-2i 3)a=z' 10t 6)r=(r+1)'z+1. 148, BiAnoqfib: 4) Ha 3 o4HElrEi niBopr,. :ittiitliillii: AITEEPA Mep3rrx A. r. ra iH. aKaaeMi,{Hnr pieexu i{li 263
  • Pxc.6 1)a=fQ) 2; 2)a=f(r)+4i 3ry=f(r 3. 4)v=f(t+t); 5 a = -f(r: 6)r/=3-l(') :.-:if il:]: I i ::t.:.!:i. 151. 154. ArropnrM ro6yaoBr .paoilla OyErirrii: rl a=nE-+: a) 6yay€Mo rpagill dryHllrrii y = G; 6) ryaOiK Oygrllrii v = G ""p"""""*o "upajr€nr,Eo IIa 4 oAnHrlqi lHra. 2 lJ=n64: a) 6y.qyeMo rps$iK OyHKrrii y = Ja; 6) rapanenbHo nepeseceMo qefi rpaoiR Ila 4 oArlrnqi npaBopyq. 3) y=G;+3. Cflo.rarKy 6yny€Mo rpaoin OyHnqii y = G. noriM noro nepeEocrMo napanerBFo Ha 1 oanfl}rqlo rpaBopy.r. OaeprKrMo rpaoiK OyHKriii , = fr i. noriM qefi rpaoiE nepeHocr.rMo napanenl,Ho Ha 3 o4aHllrri Bropy. 155, 1) y = ?; 2) Y=1 1: lt = l-; 4r u= - +6. flHqo ryadliH Oynllrri.i 2 napanenbHo ncpprrcrTfl sa I o.trxH qro BHrrJ. ro onnpy.'{Mo rpa$ik 6ttvt" y ? 1 '2r. flr<u{o fpaoi( OysKr{ir y = a rspanenbHo repeHecrr Ha I oArHrrlro ,'riBopyq, ao xc oAeDxlvo rpaoir oyHl. (ii 9 r-tl3). glrqo rpaoir{ OyHEqii , = ? tup-"rr""o ,r"Oesecrl sa 3 oAuHuqi npaBopl r, a troriM Ha 6 oaxHru6 vroD, 1o orepvHvo rpaoiK O)HKuii, ='--.--6 {4r. iiiliiiilittiii AITEEPA Mep3neK A. r. ra iH. AKaaeMi,{Hnr piBeHb ::::::: 265264 i:::l A'|EEPA Mep3nrK A. r. ra iE. AKaAeMi,{Br'tr pieext il::iliiiiiiill:i
  • t E 156.l !/ = x'1 4x + 6; g=A' 4r+4)+2l a=(r 2)"+2i 2)a= r'z+6x 6;y= (j.' 6n+9)+3; y= (r' 3)'?+ s; Io6yaoBa rpaQilla OyEtcqii 2 g= 2-' .. 2 a) 6yayeuo y= ; 2 6) 6yAyeMo r= j; 2 B) 6yAy€Mo v= ,_t: 2 r) 6yAyeMo != 2 , I. , ,l:!: jl.: 3)A=2a'!-4r+5i a =2(:t' 2t+t)+3, a-2(, 1)2+3: 4) u = O,2x' 2x 1; y = 0,2(r'? 10r + 25) 9l v = 0,2(r 5)r - 9. 3r+8 8 157.1) y=-=3', , ,, ,, 2r-'14 2t! Jt I 2, .8 'tc ' 3 x'3 - r 3' xt 2t 2t lt ,. ,._,-''rIrLI 266 l::i A'fEEPA Mep3rst< a, f. ra iH' AKaaeMi'{Hxi piEeHb :::::i::::::1t:::::::: i'.:*ii:1:il:lil:ii: UfeSPA Mep3neK A. f. ra iH. AKaAeMi.{Hrt piBeHb i::* 267 1s8. 1r ,, 4' 14 4{ir l) -lO = 4, l0 . rtl rrl .r,l' - 7 jl: (x 7) - x2 12 (t 2)s - 5 ): 2 r-2 159. 161.1) s = 0,5aF; D lt = -z"E:Z. ,l a =o,b J;
  • 164. 1) 169" Bianoaiah:2. BiAna6iAb:4. 167. 1) BiAnt)6iAb:2. BnpaB14 Ar9 noBropeHHe 171-Hexan r rpE. qiHa roBapy. fliABrqeHa qiEa roBapy - qe t + 0,25x = 1,25r ryn. Ma€Mo: 1,25r rpE. 100 %; r !pE. ! "/"; 100 a l0 0OO u 80: l0O l, -80 A =2lak.- 1.2tu 125 HoBy qiHy roBapy rpe6a 3I{]IsIlrr Ha 20 % . Bidnoatdb: Ba 20 rl . 172, I]icnn BrraposyBaHns 3anrnrr,rocs 200 40 = 160 (r) po3qrHy. y 200 r pos.Lr Hy Micrnrbcs 8 % coni, ro6ro 200:100 8= 16(r). y 160 r po3.rrHy MicrrrEcs t6.too%I fi r .oni To6rn -=toi, 160 BiAnoRiA,: 10 a . fiitiil{li::.::.::J AITEEPA Mep3rqK A. f. ra iH. AKaaeMieHrt piBeHh !ii: 269 BiAno6iAb: 4. 268 l::l: AITEEPA Mep3fleK A. f. ra iH. Ar<aAeMieHnn piBeHb ::::i:;:::::ii::::::iil:i:
  • t 173. Hexan v roqar$oBoMv crl,'laBi t lir qrlrxy, 3al'anbHa Maca rlEoro crlraBy - (12 + r) Kr. -Biacor&oBLIE BMicr Irllrrny B roqarxoBoMy crra;i crag.t"tt ', 100 % . " 12+ x SararEra Maaa HoBoro cEna3y cl(,'lana€ (12 + tc + 2, = (14 + jr) I(r. BiacorKoBr'di (2 r.r) 100 oo BMlcr qIrHIly B EoBoMy cntaBr cl{naAa€ -. iJa yMoBoIo BrAcorHoBtt 2. lpaon{ y = lflr)l 6vAy€rBcs raR: ra r{acrrEa rpa&iKa OyHKrrii y = flJ.), sria,'lexcrrE Bnqe oci Or (i lla caMin oci), saimrra€rr,c.s 6e3 3MiE, a sRa rer$,ii6 Hrxr.re oci Oir, BiAo6paxa€rLcF crMerp*iqso BiAHocHo rli€f oci. 176. Anrop rM ro6yAoBr'. 1) y = lG); 2) v = f(b) vacruaa rpagiRa OyllKriii l(ir), s&a ,!e){Crr6 trpaBopl r BiA oci y (i Ha caMin oci), 3anr.r uacl6cr 6er rMiH r BiAo6palHacrbcfl .IrMFrpr.r.rso BiA- HocHo oci Oy; 3) qacrrHa rpaoilta OyEKrrii u = f@l), axa, rcxe]lTs Brqe oci Ot (i Ha caMifi oci),3an[ aerbcs 6e3 sMi1i, a ra rracrrEa, Hrli.re oci Or, BiAo6pa- }Hacrb.s cIrMFrpxqHo BiAHocHo uiri o.i. 177 - sMicr lr'Rv B HoBoMv "o,uui ou al " = 4 "," 33 12 r x) 100 r. 100 25 Mat Mo PIBH'HH': J4 x 12 - x a : 6iftmsii, rrr{ y Doqarr{o3oMy. (2+!'4 74+ x 12+r 3' ir't Ei:.i:.: i,:i#:i::..i it:i1l::l::: 3(8+ 4rX12+r) 3 4jr(14+')-(14+')(12+') _ 0. 3(14+r)(12+r) 124' 12xltl2-xl-12xtl4t xt 1168 | l4x I l2x x'l n. 314-x')l12tx) 288 + 24x: + 144t + 12; l6At - 12r' - 16A = 14r. l2r I =0j 3(14+'X12+r) x'-26x-tzl ^ [x -26x-]20=0,= (,: l 3tl4 rr.)(12'.r) (14 x){l2.ir), 0. Po3B s,l{eMo piBHflHHr I x' - 26x 120 o, D t69-120=289, 4 = 13+17=4.x,=-13-L7= 30,t=4 BianoBiaa€ yMoBi 3ana'd. BiAnosiAb: y rrosa'rxoBoMy cflnaBi 6yno 4 &r q!,rrrcy. ForyeMocr Ao BllBqeHHg HoBolreMx 3A=r+7it:=3! 7:174.1) "3 ro 10 10 I02'=- t tt: " tt : t-2=-t t t2lx/,li " t 2 ' x-2 .Y 6 u 6 r:--= t- fry u*--'=tr g-t=!-'": Stgtll Lx+2:'5"5 25(y +1'=r.+2. x=25(u + 1)' 2(r> 2,y> 1r; I I 1 1 I 1 I a-. 1 c-o I o. a. 4l --=-: --=- - -i b=- O 'a h c b t a b K b ac c a (a+O,b+0,c -O,a+c). Konu 3po6neHo ypoKl,t '175. 1. rpaoiK y = l(t) 6yay€r6cs raR: ra.racrlrHa rpaoiKa Ot'EKqii y = l(r), sfta ne- )Icr-rrL rpaBopy.r Bia oci oy (i Ha caMifi oci), sa-'lsllla€rbcs 6e3 3MiII i Biao6p&r€€rr, cn cnMerp[.rHo BiAnocno oci Oy. fia. a=lx' 1) -4 z-, r.? u zt a=)G-zl n, "=l "" l'-t 27o it;:t::. ,.IIIEEPA Mep3neK A. r, ra iH. A(aAeMi.rHrr pleenr :iii:i:i:iii:i:i:i:i:ii :it::iitili::ilitl ATTEEPA MepsnrKA. r. ra iH. AKaaeMi'{Hrr piBeHb li::it 271
  • f lo Airopl-rrM no6y4oBlr rpaoina OlBlrrii y =': I : XL 2 1) a= : 2 a== 1 (Dapanenhflo nepeEe.eMo BHt{3 Ha oalrnxuo)i 3) A =la -1 t.{acrrrEa rpasira OyEXuii. sl{a ne}rnrr, Bnlqe oci Ox a6o Ha oci O.r, sanrma€rbcs 6e3 3Mif, a ra qacrrtsa, i Ot, BiAo6par{a€rr'cs criMerpnqno BiAHocHo oci Ot). 179.1ra=@ t)'i rso. 1) y=r/r+21; 3, v=,tE-rl+2. fpaOiJr Oygns,ii lt = ,1, tl , 2 clrMprpvqHxfi Bi.qIIocEonp€Moit=1. 1 4) u = --=_.'- ix+11 3 .1l Dadrk rhvHknl '" " .r+1 3 crMerpr.rHz ii BiAsocHo npnMoi t = -1. Itijh:Uf::i )i::c+!!:.1 i,:i; .llt: 4, O6epfleHa OyHKqit 181, a), B) - roMy u]o r MolrcHa oaEosnaqHo Bnpasr{rs qepe3 y sa o6nacri sIIaqeIIl, 3anhsoi oyEKqii. lA2, a), 6), B) roMy rrlo r MoniEa oAEossaqEo Bspa3nrl-r qepes y Ea o6nacri sEaqeEb qa,qaHoi oyr$cqii. 1A3. D A = l, , , e n, y € [0; +-). OcFiinErc.r r Ee Mo]Krra oAHo3Eeqso Blrpasltr]r qepes v Ea o6nacri 3EaqeEr, sa,qanoi abysxqii, ro Aana OyEnris fle e o6oporEo1o (Hanpu- &''.aA,V=2,ax=-2it=2). I 2) u=+, xe (-*;0) u (0; 1-1, g e (0; +-). OcKinr,RrI, Ee Mo*clra oAIioBEaqHo Bnpa3rrrr qepe3 y sa o6nacri sHa.reHb sa,qasoi O}.Ir&Irii, ro Aalra Oylrriqis Ee € 060- PorHolo (1lallprRra.q, Y = 1, a t = i:1). 3 a = 5, r e R, v e l5l, Octiinbr r t He MolrcHa oasosrraqtro Bllpa3rrlr qepes y Ha o6nacri snaqellr, Ba,qasoi OyHftrrii, ro Oys(qis y = 5 Ee e o6oporlroF (I{anpuKnan, I s. a .r = 0. 11 ra iHroi). 184.1)!=3x: 1,xe R,3x=V +1; t=g-!, ge RlDlxl=r(y,t. nosHaqlaMo B oAepniaEiii OopMy,rd apryMeEr qepes t, a ibyHKqiro .rep$ y. MaeMo OyHXqirc 11 s==x -, sl{a. o6epHeHoro ao OyHHrii, = 3i l. 1 2t u = 1, x e (--; 0J u (0; +-.). OcnirE(Ir Ha Bcii o6nacri Br3HarreHss AaHa abya' tt Ktrifl o6oporHa. 10 Bl4paxa€Mo.r qepe yr ( @i 0lu(Ui i-1. i:iii:,1!{iilliii LnrEsPA Mep3rrl< A. r. ra iH. AKaaeMirHrr piBeHb .allj 273 zt v =',Ei; 2Jy=(lx-2-1)" 272 ',:* NllEEPAMep3ncK A, r. ra iH. AKaaeMi,{Hrr pieenr' lll:ill{ili:iii:i
  • f SMiHroroqrr no3Ha.reHHs Ha rpaArqirlHi, oAepniyeMo 1l ,l )..at u= it. 2x-r.0.'=;.'.1, -.;) l;, *J. Hasci;o6.1a.rioy Kqir o6oporna, ocllinr,Kr s lirnrrrrro y = ! MoxHa oAso3HaqHo Bupa3xrx .r .rep$ g (y + 0 Ha o6nacri 3naq€Ilb 3a.qaEoi OyHRqiI). orxe,2r-1=1, z,=!.'t, zr=!'u, r=t e,,,,o. 9C92!' nosua,r Mo rpa,qaLlifin., o t !' ,ur rDyHK(ir. o6ppHeHoo !o OyHKuir t"' " z'-l tl At U ;x t 4. r r R. I{a sciii o6nscri OytsRuir o6oporHa. 60 3 piBHrHHfl y r'i 4 Mor{Ea oAHGrravHo Br.rpa3urrI r qepe3 y: v= g-4:.x=3c- 12. Iloosaqrr,{o rpa- ,qxuiiiHo:|] =3x .12.te SyHKrir. o6epHeHorc ao.byirxuii n j- +. z,c I. x 0.ro,ais o.spiBHo.ri s ] "".*., ri$=r, vr L. ./r-Jra ItpaxoByroqx. qora yuoBo,o y O.Ma.Mo r=]. n."**"". tpa.qlqiiino: u I rr ' U. y l,t. Ur OyHRuis o6epH"r" r. Orr#. 3, a = 'lr"-.3a yMoBoror(y) = [2j +*), roai y 2 0. 3 piBEocri s = lFJ MaeMo. s'=i 4i t2= y!-t 4; r=!,f}i, ane.!€ [2; r-1, 'o-y '=.,[t*a. nou"u- .ra€Mo rpaAxqiiiHo: U=.lF+4 Q>O,:(>21. qs dlytlRrris o6€pHeHa Ao Aauoi. 1 IIs OyH(qis o6epHer$ 186. Il u=-L. r+ oc&in6xE B piBH.sHHs l, r e (--; 1) u (l; +-). Ha Bcii o6nacri Oyrxqis o6oporHa, I = ---:-: MoxHa oaHosHar{Eo Brpa3rrr jr qepe3 g. !(r - 1) = .r. 188. 1) (DyHKait yt(r) o6epHeEa Ao OyEtl- qii V(r). rpaoiKn OyHnqir; cxMerpr.r.rHi BiAEocHo 6icenrprr$r l. 3) g = 1_ (DyHkuir ,,(rJ o6FpHeHa lzx, t < u. ao OynKrrii y(r), ixHi rpaoiKn cniBtranarorb, FRUro.f,:0: a flKuo.r' 0. BoHu CrMeTphqHi BiAsoc[o 6iceErprcr l. 149. 1), = 3t - 1. @yHXIti.s yr(t) o6ep- neEa Ao QyERqii y = 3r - I, ixsi rpa, Oixu cuMerprqsi riAHocEo 6icexrplrcq I i III r.oopansarr[x KvriB. 2) @yHKrrie !,(r) o6epBeEa ao OyHR- qii y(t). fpaoi"t OyHXqifi cuMerplqEi BiAHocHo 6icexrprcr l. 2 v = r' - t. oyHxaifl y,(r) o6epHeHa Ao OyHKqii U = )c' - 4. IxHi rpaoit{Ir c[MerprrrHi BiAsocro 6icerirp cr{ I i III KoopAuHarssx nyriB. gx c x, yr r = U. xtg 1t = g. , ! .. g, l. norHaquMo rpa{ruiiHo: vt.. , r l. olpuvatMo oyHK(r'o. ooepseHy,4o aaHor. . r [r , 2ta J2x 1,2! lzO, x,:, Dtcl l;t r-1. Ha rriii o6nacri.r MolxHa oaHo. 2z 3HaqEo Bnpa3xrn qepe3 y. Bpaxoryrcqr, rqo y > 0, Ma€Moi y2 = 2a 1;2t = g' + 7i r=?. no3Ha,r,rMo rpanuuifiHo: u=-- - ur ibyHxrIfl o6ep:rera 4o rblr. I{uii y J2jr l. 3)C=2Jx t, r > 0, r e [0j +-), y € [ 1;0) (r oaHo3Ha'{ao Mo}rcna Brrpasr.rrr.r qcpej y).3AaHoi piBsocri Maer'ro: y+l=2./r, Bpaxosyror .r yMoBy, + I >0,ro6roy:-1. 1-I onepxrfMor (y I ll: - 4r. x-'llJtlf. nosHaquMo rpanhqiiHo: g= Otx rlf. o,qeplttvMo Oy,rKrilo. o6epHeHy Ao AaHor. qu=r!,D(yr=( -;01, roAiy > 0.3 piBEocri g/ =r? rpn y > 0 orepxyeuo r = tJg. BpaxoByroqr, qo 3a yMoBoo r € ( *; ol, Ma€M. r = -u[. n*"rr**o rpaa'qiiiEo: y = -G. U" Qysxqis o6epHena ao aarioi, srca 3a,qaga rirbnr Ans, € ( *; Ol. ft7., y=!12, r€ ( *; 0) ..-l (O; +-). Octinlnr r oaHGHaqHo Moxlga B'pasrlrn qFpF3y.roirr x 2, ux x -2.xtu ll=2. x=:t,g-1. Ilo3EaqaeMo rpaArqifiro ii orprrru"*o: y = _f . Lls iDyElcqifl o6epse!.a ao aanoi. 274 ii:i AIrEEPA Mep3nsK A. f. ra iH. AKaAeMi,{H}ri piBeHb ::i,;i::i:li:!:i;:i!::: i::::illiiiit::ii: AITEEPA Mep3rsKA. r. ra iH- AKaAeMiqHy.y. pi*e{h r* 27i
  • ["G. " : o. ar y=lr lt.r. .r < 0. Ipa@ixu o6epaerrx OyHriqifi v(r) i yr(r) ctr, Merprr.rHi Bi,qEocHo 6icekrprcr I i III KoopAn- 195. Hexan 1 - po6ora, roni rep a rpy6a 3a g roAlrH HatroBlrne ] oo euy oacenna, rrI.Jr 3 ro,{r{sl-r loHa nanoBHro€ : 3 =: o6'€My 6aceiiHa. Apyriii rpy6i 3arlrllrnrloca 93 ranonsur{ f - i = i 06 eMy. BiaoMo, rqo apyra rpy6a EanoBnlo€ 6aceiiH sa 12 ro- nHH, roAi 3a 1;oo,;v ".r" ","""",rr I ooc'y,, I o6'cuy eona 'anoa,r,rtr .,^ 1,+- I rz s 1"oo,u1.su"",loovie'"a,,o",,""o"lt*t=11 (,oaxnr' B;dno6idb: ra IL roA!,t}l. 196. Hexafi Apyra 6pBraAa Mo]rte sopar,r rone (S rlroqa) sa J' roArE, roni rep- rrJa - 3a (, + 12) roar.rE. 3a 1 ro,qnHy.qpyra 6pErara MoJ*ie Boparlr !, u ,r"p*" st r l2' ToAi pa'oM Ba l roar'y BoH' Mo,{yrr, 3oparr, 9 * "r - = "t1 * '.1]) = "'. 12! , ' x r'12 ir(x. 12) "r(r+12) vce none pasoM BoH' Molriyrb sopa'r 3a s , s(i* *,ll) "oaoo, ro6ro sa 8 roalrH. x(x + 12 MacMo DiB,,EHr': s , 2sl' *-9.1 -- e, r(r I 12) I' x(x - t2) 2(r 6) '2 +2r=16' + 96; r* 1; x'z+2r-L6x-96=O: r' 41 96=O,orxe, ! 12 a6o x 8. 3a 7 roArH vot+re soparlr nonc Apyra 6pHr eaa- e neprJa s. 12 + 12 = 24 (toAt E). Bidnosidb: 12 roa H i 24 roaHHr. 197. Hexan trorpi6Ho IlaroBllrrs 6acenn (1 - norc o6'€M) i nep a rpy6a Mor{e Ha- noBHrrrr-r ioro 3a .t ronrH, npallloloqlI cauocriitro, a apyra s (:. + 24 toELr'J 1l 3a 1 roAttHy neprra IlanoBHroe i, a aovra _ 3a 8 roam po6orn Apy- x24 ra rpy6a ,rafloBxro€ j^,. ". 1 fo,qrrEy, npaqrolo.ru pa3oM, rpy6r HatroBrrolorl' '" x+24 I I ^^(r I ) ,t ,tro. roai 3a 20 ro.ar-rH 20 lrtrrZq). Tarir-rM.rrIIoM, 3a 8 roalrs po6orr.r apyroi rpy6r{ ii 20 roallH cyMicroi po6orll repllloi t ir apvloi rp6 B,rxoHaHo : po6orH. Ma.Mo pisHfl'rHs: s /1 r ) 2 14 10 r __2tt.t - __f _I : r-24 : t,24) 3 r-24 ir 3 42. + 9Ot + 72O= t'+ 24r, t+O, x+ -24| x'- 48 x 72O=O; 4,=24r.17296 r,, = 24 t 36; ' = 60 a6o it = -12. YMoBy sanoBoJtEEs€ qlIcno 60. 3a 60 roarn MoJ{e HatroBHtrlr 6aceiis nepua rpy6a, a Apyra - sa 60 + 24 = BiAnoqiAb: Ba 60 rcllrl{ i 84 roAnEr. 5. PiBHoclrnbHi piBHgHHq. PiaHeHHg-HacriAoK. PiBHoclrnbHi HepiBHocri 194. 1) Ta&, 60 Ha MHor*{rlri (-€; +-) t{rcno 8 e xopeue*r i repEoro, i Apyroro piB 2) TaK. i:iiii:.ffi;fliii:jiuresPA Mep3ncK A. r. ra iH, aKaAeMiqHnn pieeF.s l;l:l zzz 191, IpaOiKI, o6epEeHrx rbyHr{qin y(r) i y,(r) crMerprr.rEi BiAEocEo 6iceB rpr.tcr., L. 192. y = kx - b, k + O. O6,racrs e[rnaqeHin -4. OcKin6RU r oaHo3BaqHo Blrpasrrsqepe3 v,roh'=v b,,=+, "=it-i leni',nHa3a Hicrb, sa yMoBoro fr + 0. TaKrM qrrHoM, o6epseHa d}].'HKqis a,= ia ; Nn qii v = kr + b reri € niEifiHoro. 193.3a yMoBoro y = l(r) - HenapEA Oyllnqis. Hexarl Ol.llltqis y,(r) o6epHena Ao Aa- Hoi. fpaoil{r.r qI-Ix OylIxqifr cr.rMerpr.rsi BiAHocEo 6icellrpncs I i III &oopaslrarsr:( RyriB. IpaOiK Aanoi Ot'EI{qii cnMerpr.rHri BiAHocEo ro'rRn O (0; 0), roMy ii rpa$iK O]'EKr{ii yr(r) re'rc cr.rMerpr.r.rErii BiasocEo qiei rocKs, ro6ro y,(-r) = -yr(r). OrrRe, yr(x) c EenapEolo SynKai.rc. BnpaBx Arn noBTopeHHq '194. Hexan.4 [4 > 0) - ycs po6ora, sriy rp€6a BrrcoEarr. flepnllIii po6irE{x Brrco- Eye Bcro po6ory sa 20 roarn, ro6ro sa I roaagy BiH ""..""" +. Aplr{n po6ir- 2V nrrc BnrcoEye Bcro po6oay Bs 30 roAn$, ro6ro sa 1 roAr.rHy BiH BrRoEy€ jl. Pasou AA50A5A--'"303a I roAr.rsy BoHr.r Br.r(oHyror6 20 1 30 60 6 . v.rc pobory pa3oM BoHH Bu- 5A_6,46A:6 roAxH. lobro - =;=l.z r-oAxBu. BiAnMiAb: 3a 1.2 ror]j]l r. 276 llliAIrEEPA Mep3ncK A. f. ra iH. AKaaeMiqHr4i piBeHb
  • 12) TaR, 60 na Mso}I{I,IHi ( *; 1) -r (1; +-) trepDe ii apyre pi 5) Hi. 6) TaIi. ?) TaK. 8) Tal{. 9) TaK. 2OO.7) 2x - 3 4, x ts R. -r 3.5. fioMy piBHocn,"6He pisHsHHs -r 3.5 = 0: 2) lxl = 1, r. R, r r-1. iovy piBHo.xnbse piBHaHe r I 0: 3),r+6=,r-2,re R.0 I 8 xopeHiBEeMa,. ioMy piBso.xnbHe Esr:+1=0; ql L I O, r F { -; l).r (l; r€), KopeniB Fe va€. rl iolay pinnoca,r*re piBHnHB' ;- ; o. -I-I czoci6. Apyre piBlrnHHs 4r - t = 8 + 3 MoJr.I{a oA€p{arl{ 3 nepllloro 4t 8 = t + nl(rrlo Eepen€crrr AoAaHRr s oAniei cacrEEE piBHsHns B iHtrry .racrr.Hy 3 nc)rHrvr 3Ha,{aMl,l. ToMy piBErHur pjBnocHn6Hi 3a reoppMoro. e KopeEnMtr nepuroro piBE.sEHs IIa rii caMiri MEor.c1-IIIi. a) 3'r-5 'r I {treourc DiBHnHHrr:9r Ib jr 6i gr '21, r=11 .10r.. 26 18 HrrrHr Lr ls ,r = 6 re]:{ Mac KopiHb r. ;. Orx.. Ha MHosHHi I -r qi piEEsEEs piBllocrn6Ei. (A60 Apyre piBE4sEs Mostsa oAept{arlr, sKrr{o o6tABi qacrtEr nep oro Ha 6. 3a reopeMoo 4i piBll.sHss piBnocrnbHi.) 4) PiBIrsnHs (2r + lr(r' + 1 = 3(" + 1) t 2t + 1 = 3 piBEocr.'nbsi, 60 apyrc MoxHa oAepr{arr.r s nepllloro, sRnlo o6BABi q6crrs6 nepuroro piBErHEfl noAinnrr Har'z+1+0(reopeMa). 2O2.1r Ia'/".2) Hi; 3) Ei; 4) tri; 5) raE; 6) Iri; 7) lri, 60 ftopeEeM piBHnHEs 2r + 1 = 5 e.ircno 2. ,firiqo o6taABi rracrsEi riboro piBHFIlEn troMEornr.rr IIa (r + l), ro oAep*cr Mo: (2r + 1Xr + 1)= 5(a + 1'), 2r' + tu + 1 = 5x + 5, 2x' 2x - 4 = 0, r' x 2 = 0, 'to6ro t = 2 a6o )e = 1. Or)rce, &OpeEi apyroro piBHnHHn ne € xopeHsMn nepnoro. 203, 1)r+ 3 > 6; r> 3, re (3; +-); 4r< 12i x > 3, r€ (3; +-). Ili sepiBEocri € piBEocrnbEzMrr. 2) (x + 2)'z(r+ 1) < O ir+ 1< 0 ae e pianocr-r.rlEurrur-r, 60 MEoxcnEom posB's36iB nep oi irepilsocri € r € ( *; 2) u (-2; -1), a Apyroi - xe( *; 1). 3) (r + 2)?(jr + 1) < o, poBB'ssKoM € MEo,r{r{Ea ( -; 11, a posB'ssnoM sepiBHocri r I ' 0 ( MpostsHa ( *: -11. Orxe. qi RepiBHo.ri 6 piBHocr{nLts vs. 4) Po3B'sBKoM HepiBEo"ti 1.1, 1 a.0 e MEo!@ira(--;O)u(li +-). P$B's3rcoM HepiBEocri r > 1 € MHolcrHa (1; +-). MHorrorEu IIe cniBfla,qaorB, roMy qi lIepiB- Hocri He e piBHocrnbExMr. 5) Po3B'.a3rcoM HepiBHocri, x'> x, x2 r>0,i.(a 1)>0€Msonrl-rlla(--;0lu[1;+-); posB'.sBKoM EepiBEocri r > 1 € MHo{r Ha [1; +*). MHoninlrn He ctriBtra,qarorr,, roMy qi HepiBHocri Ee € piBrrocrri6srMr. 6)(r+4)'<0, re 6:lz 2l< 0, r€ Z. HepiBsocri € piBEocrnbHr.rMrr. 2O4.1, (x 3t'(r + 4) < 0t r + 4 < 0 t x 3 = 0j r < -4 i ' = 3. MEo,IlnEoro posB's3rdB e MIIoJxrHa ( -j 41 u {3}. PosB'ns$oM EepiBnocri.r + 4 <0, r<-4€ MnorrcrHa ( -; 41. HepiBEocri He € piBsoc*rnr,EnMlr. 2) @ 9l'(x + 4) < 0; r < -4. MHo}I{rHa (--; 4) e po3B'ssnoM qiei EepiBHocri. ,4r.8 EepiBFocti t + 4 < 0 po3B's3KoM e MHoxcnHa (--; 4). Or)$e, qi sepiBnocri 31 {--? ' g. pooB fl3tsoM c r'r'o)nrHa (-*; 2l (4: --).x4 --. -,.-- -Y-- , 41 1E < 0, posr'saxoM e .rxcno 0. ra < 0, poBB's3KoM € qrcno 0. IIi HepiBsocri piBHocrrnLHi. 205" 1) PiBEsHEs x'= r e EacniAKoM piBr.sIIIIs r = 1, 60 lropirlE 116010 piBEsHEs e Ko- peEeM piBHsHs.fi r'= r, a"re se xoxes xopinr piBHeEHr ,v'z= x € kopeHeM piBEsHHs 2) PiBnsEEs 0 r= 0 e EacniaKoM piu""""" {=f. 3) PiBFnEHn I'9= I € HacniAnoM piBHsHHs x3 = 1. 4) PiBEnEEn ,r = 1 e EacniAKoM piBnssrs.r3 = 1. 5) PisunrlHs r'?= 36 € nac,rirxou pinsgssg {1= 6) PiBrr.sgrr.a t'= 4 e qacniarcoM piBHngns .'--!= = l-J=. t+2 x+2 7) PiBHslrHs:t'- 1=0 e saciri,qxoM pin""""" t'=-0. lri:l:iiiilti{lti: AITEEPA Mep3reK A. r. ra iH- AxaAeMiqHan piBeHb tii: 229 Ans nepiBHocri, 2> O, r > 2 posB's3KoM (2: -). Ui HepiBHocri Hc c piBHo- 3) Hi,60 Ha Msor{nHi (-*; +*) repue piBEtHHs Ma€ oArH liopillb, s&ai AopiBnm€ 5, a apyr. piBseHHr - ABa xope$i: 0 j 5, roMy RopeHi npyroi'o pisnnFBq nF. Ro- peEsM! rep oro. 4) TaIt. 5) Ta&, 60 aHi lep e, aEi apyre piBEnEHn Ee Maror6 riopeHiB. 6) Tan, 60 trolcrre s piBnsHb Ma€ 6e3niq nopesiB fi o6tABa piBEsHEs 6yAr,-nfti BEa.reliss t. 7) Hi, 60 &opeHeM rep orc piBEsIrEs Ha MEorrinEi ( *j +-) e qucno 1, a Apyre EqEEn Mac pra KopeHi: I i l. 8) TaK. 9) Hi. 10) Tax. 11) Tax. nopiEb .r - l. roMy BoHU pisHocMi6lri. 13) TaR. 199. 1) TaI{, 60 KopeHeM xoEclroro s l{t{x € qrcno 4. 2) Hi, 60 Depne piBHsHEs Ma€ aBa rcop€Ei: 0 i 1, a Apyre piBHsEEn oAxn HopiEb x=1. 3) TaI.. 4, TaK,60 r{oAlte r piBHeHb ne Ma. HopeHiB. 2) PiBHssEE piBsocrnbni Ha MHor{nHi (-*; +-), 60 (opesi repllloro piBEnHHn 2 i -2) € KopeEsMn apyroro piBri.flEn.n, i EaBnaKrr: &opeEi apyroro piBlI.sHH.s (2 i - 36 r-6 278 i::IiAIrEEPA Mep3rrKA. r. ra iH. AKaaeMi,{H]4t piBeHL
  • 206. 1) PisssEgs.!'=.r s sacrirxotr{ pisHalrlr.E 5 = 1. 2) PiBssHHs r(r - 1) € sacriAkoM pilHsHss.,.'? + 1 = 1. a) piBH'HHe ,r, = 64 c Hacni!{ord pt""'"'" _i.8 =;], 4) PiBHeHHn r:=9c Hac,linffoM piBHflBHn r^- J ^ s, 1-. a+3 ,+3 207. 1) PiBHsHs.s 3r - 5 = 1 piBEoc',rElre piBHssEIo t = 2. 2) PiBssHss (:r - 3)(t + 2) = 0 piBEocrnEEe pisHgHsrc i:'- rc 6 = 0. 3) PiBnsrIIIs 0 . r = 0 i 3r - 5 = 3t 5 piBlIoclrnblli. 4rPiBHqhHr0 jr- I i 0 .r=3 - piBHocr,rbsi. 208. 1) (' + 3)fl') = 2ltl + 6, (jr + 3)(flJ.) - 2) = 0. IIe pi:gssgg naae KopeEi '=13 213.1tx,+t-6=0, x,+x-6-(r+3)(x-2); x,+2x-35= ( t2-2x+ 35)= (r+?Xr-5); 3t2x'z t gx 18 0:D=81 -4 2 ( 18) 81 | 154=225t,r, = -9-15 '4 ,"= j#=+= 6; zx, + er . 18 = 2(x - |)r:u + o) = rzr-axr+o); 4) r' 16x+3=OiD=16' 4.5 3 = 256 - 60 = 116; ,, = 19# = 'f, = +; ,, = tu;tn = r. sx" - rc, + z = s(t |)r,,r = ru" - rx" - rr. 6. MeroA iHTepBaniB 214.1) (i + 1Xr - 2Xr + 5) > 0; r € ( 5; 1) -/ (2j +*); 2, x.(r 3)(t + 2) < oi r€( -; 2)u(0i 3); 3)(r+7xjr+5Xr-9)<0; J' € (--; -71 u [-5 91 4) (.t + 3)(, 8Xr - 10) > 0; r€[ 3; 8] u [1; +*); 5) (2, + 3X3, 1Xr + 4) > 0; /r ) x€( 4 1.5)!, ::+-: 3 ).. 6) (2r - 1X3 jr)(ir + 1) < 0; r€( 1;0,5)u(3;+*)i 7) (r 6)(7x + 1X2 - 9r) > 0; ( 1) x € :; _ = l_r [4,5; 6]; 8) (r 3X2r + 1)(1 5a)(:r + 4) > 0; f r fr rF 4i -Lrr -:il,2)5) 215. 1) (r + 3)(x - 1)(.! + 4) < 0; t € (--i -4) u (-3' 1)' 2) (t - ?r(t + 8)(r - 12) 2 0; r € [-8; 7] u [12; +-); 3) (3r + 2)(, - 5)(4r 1) > 0; / 2 r.r el- 3: aJU rbi + @); +.r, = -1. fr= a. 'x,= 6: Lx=2i 2r-35=0; lx, 2135-2x-r'=0; )r, + x1= -2. lx = xr 'x, = -35: I r. = 3 2' /lii:l:.:{.!:.i:,!! it:l:i'i-:a.a:.i::::i:: i Rop€Ei piBEsEns f(t) = 2. ToMy, sftqo qe pitlrssHJ' 3aMin'rr FIa piBHsEEn l(.t) = ro Mriox{{Ha xopeHiB BBysurLcs. zt,gn.qo pluoono" I(') o raMiHr.,ru Ha piBusHss f(.r.) u. ro MHor{,rna t'+1 3) PiBETIIHS (r + 1)l(r) = r. + 1, n&e Mo)KEa sarrcarta rall: (.]r + l)(f(r) 1) = 0, rrMe 6irBrrle nopeEiB, Hi,{ piBEsHEs t(r) = 1 (qe r = -1 i (opeHi piBEn'isn flr) = 1)' ToMy MHor$rrHa xopeHiB sBy3rrr.cs. q f(4. c(x!. Uc piBHauH' Ma€ kopeHi. nxuro x F -1. PiBh'HHt /lx) = s{.rr'i+1 r+1 6i,rblll xopeHiB. Hi]l. raHe. 1ory MHo)}{HHa nopeHiB po3llrtrpltrLcs. 209. 1) HepiBHicrb r < -4 € EacniaKoM rrepiBEocri x < 1. 2) HepiBHicrL r > 5 e HacniAEoM IlepiBlrocri, > 5. 3) HepiBgicrb r' < 0 e IracniAKoM EepiBnocri r < 0. foryeMoca Ao BnsqgHHg HoBoiTeMx 211,1)(r-5)'z>0,r€( -; 5) u (5; +*); 2) (t - 5)'> 0, , € ( -; +-); 3r(x.-5t'<O,)c€A: 4r(x-5)'<0,x=5; s; I :-l | > o. r.. ( -: -5,,, r-5: 5r r. (5i -t: o; lll >0. ie ( -i s)L,r-5:--r: .r+5 t r.'5 2{r r5l - x-5-2r-10 ^tt>-'-<u.<u.'xtb 2 zlx -51 2tx+5) r €( -; 5) ! (-5; +-); 8t +>O. jr€ ( -r O)u(0: +-l; sr *:0. r=n.x'+ l 212. 1) Ocxi"nrxu .r e (2; +-), ro sEa.{elltls Bvpa}y , - 2 € AoaarrilrM; 2) oclcirbrir r € (-3; -2), ro sHa.reH1is Btrpasy x _ 2 € BiA'€ME!iM; 3) ocEinbrir r e (--; -A), ro 3lra.reEns Brpasy x - 2 € Bi,q'€MIrnM; 4) oc&irErcr r e (5; 9), ro ssa.resHs BrIpa3y .t - 2 € AoAarH{M. 28o llJ: AITEEPA Mep3reKA. r. ra iH. AKaaeMlrxrr piBexu lililillli::,'.:i;X -GG€5 1 - -,,-=7':/--+j--ffi-: - -)/-_. -Y--- -Y-a - -7-50:t ----Y--i/-=)/-+ , 3 a 10 x - - ,--F/-:-/'-- ti---t-i-23 ---T-,.-- -,--f-z-- -1 --;/' ,,--T,,---+-------- + -1 4,56x .7 0,5 .x 5 .r+5 -<u. 2(x + 5) 2(jr + 5) -4!!3 215 E4 --./-iv. ,,-+---1i----i--1'- r ---Y-lr-=Y- -a712 -----l 7_i /-=' /7 ------{.--------fF - l< :iillliilliliii A'IEEPA Mep3rrK A. r. ra iH. AKaaeMi,rHrt piBeHb tl! 281
  • 4) (1 3'Xjr + 2)(3 - t) < 0; /r ) r€( -: -2)ula:3]i 5) jr(s rX6 - r) < 0; n€(-; 0l u [5;6]; 6, r(sir 3n2 ,ll1x 3l(.( 5) 0: rEr-: 5r L I , ?, ol ,19, ,1. 5 ,r 4 ,/ 216, 11-<0, r€ ( 7;8)r z; 11] ' o, ' € (-*; e) L, (11; +-); 3, ' -2'4 o, ir ( --; 2,4 | (3.7: -): ar -10. r€ [ s.2i 1.,1): 5) -: 0. r € [5: 6]r 6t 6r I 3 6 o, ir - ( -; 0,6l (0,5: -):2,5 - 5' -. {r + 15Xr. - 2) - ^ r-15 I _<U. r.€ {x + 5l{r. I6) rir + 5.4nr + 4.2) ^9t 2U. (12 - rxx 4) r e l-5,4, 4,21r 14;12). /--+--?-- -/- - ti3 a +' -..-"-,,- 1i€ 53032)c 54 -=- .,-'-,. I 11 r----y'---.:1,'= - 2,4 -,i -:-{+ =-J'1-fl-0.6 0,5 - )/-tr)/--)t- . 1s 2 15 ' :.zfr.- -)t-+ - 5 3,8 16' )r+-Y--v?Y-,-5,4 1,2 4 12 r + -..-- € -3 1ic l---,-- --,,'- + --j -; - )cG41 ,4 --Y-li--ra;-r,2 1,4 1,6 -AAr-1,3 1,9 2,3 '' 13' ^2r4--ll .0. " .f r, il t,,0,,(x + 3Xr 1) I 3,/ sr latlq llso.(8 + xX10 r.) r € ( *; -8) u [-1 ?] L, (r0; +-); u, (x+1)tB rt ,n (3x 2)(4 3,Y) /n r, xer-: 1lul1;:] uta: +*r. -7zl/- ,'-i/- 3214 3 - /-? ,-- z-+ Z-t+r--r a17t}x -1 243 ';:l !ii::!i i ii:':i.:.!!:.: '::l-!]i!it:. 2'tz.tt * 1 ,0, '. r -;.3, (t; -):i-1 21 L. g, xel2:o)i 3, :] 1>0, r€( -i0)![,t:+-]r {x 2l(x+1) <0. r€{ -i 1tu{2:4)i a4 (r+1,2Xr-1,6)<o. ;n 1,4 ( -r 1,2] L/ (1,4; 1,61; ->ll (1,I rX, - 1,3) (-*; 1,3) !r (1,9i 2,31; 2) (jr'? 6rx.r' + 5n - 6) < 0; r(r 6xir + 6Xr 1) < 0; rE(6;0)!r(1;6)i Jr {x 4.r 3)(jr' 31 2) 0i = - -l (r 3)(r lxx+1Xr+2)>0; -ffijr€ ( -; 2lu[ 1i 1]u[3; +-); 4) 4r1 - 25r 0: x(4x 25, 0; /'---'/'--/'| x(2.r-5x2'.r-5)<o; + a--;--"r. € (--; -2,5) u (0j 2,5): - x-4 - lt 2x 2t -5) 0. .0. r-v.-,/-l,,--Zi.' I (r 3)(r 3) --i. !-l re(-; 3)u( 2; 2)u(3j+-); -3 2 2 3 a r' 3r rrr 3r 6) - r0- : -' 0- --:,.-- /-- 7---,.-_ J. ar ; (r i,(r l) ----.-1- t- irE t0; r)ut3;7); 0 1 3 7 7) '=-:'- ' :0, l) 2x 5x 2 o, D 25 16 - I,r' ,1r 4 5+3 5 3 l , - - 2. 0.i:2lrr 3"r-1=0,'4'42 lx I 3. fr a. 2,r.-2xjr o.b, ^ }A'QA€- lr r 4t ! l: rir 4r{x lr v l I 2 4 t r € ( -; l) u lo,5;21 u (4j +*); 2 - x 16r - xtx' 76t 8). ..0. -::: - 0. -./-../---",'/'--,,-jr r 30 tr 6X r5, ,rr 4lrr+4i 5 -4 0 4 6 x 219. 1) (:,r': 6axr, 10x + 9) > 0, (r 8Xr. + 8)(.r lxn - 9) > 0, r€ ( -; 8lu[1; 8]ut9; +-); 2) l" + l;@'z 7i. + 6) < 0, ir(x + 7Xr 1)(r 6) < 0, ir€ ( 7;0) u (1; 6); x! t 12 rr+3lf,-41 lJt _ <0- <{l- x' 36 (r. - 6X.Y + 6r r€( 6; 3lu[4;6); 7 _T)AOG4 6016 -)f-f-.)/-)/-r, --i,,- ,?-./=./- + l-V-)/T-y-Y-,- 6346 [ 15i 2] u (15; +-); ( -; 5) u [3,8; 16); -84) 5) 6) --Y-1rl-G€ 218. lll 2l{n' lr '0: (x 2)(-r I)(r l) 0: -V----.-'---,, x € (-2; -1) u (l; +-); = --i-i - 242 iiii: arregpl tvtepsneKa. r. ra iH. AKaseMiqnr4i pieexr iii::::i:;l:iiffii;: i::!:ii:!ii:iiiiij: AnTEEPA Mep3rrK A. r. ya iH. AKa,qeMi,{Hrai piBeHb iai::t 293
  • T 11 - /-: /- /l ,.-l I a{ J--.....a',1---- 5) (.' - 3)'(x' + x-2,<o, (r-8)'2(r+2Xr-1)<0, x e (-1; 2r; 6) (a 3),(r, + t 2, < o, rx 3f{r 1)tr 21 10, rE[ 2; 1]ui3]; 7)(:c-')'(t')+x 2)>o, (r.-3)'(r-1)(r+2)>0, r € ( -; 2,) u (1; 3) r-, (3; +-); 8)(,r-3)'z(r'2+'-2)>0, (r-g)?(r-1Xr+2)>0, r e (--; 2l u [1; +-). 223. 1) (r 1Xr + 3)'z(r 2) < 0, x e (1t 2ri D, 41(x + 1X' 3)>0, jr € ( -; 1) u (3;4) u (4; +*); 3(2r+ I'(r'z 4, + 3) > 0, 1) x, - 4r+ 3 - 0, fx,+',-a. lx =1. 1,, *, =a, l'=a, (2!+1),(t-1Xr-g)>0, , € (-*; -0,5) u (-0,5; 1) u (3; +-); q Qx + t)'b 1)Qe 2) > o, r e ( -; -0,51 !, [ 0,5; 1] u [2; +*), ro6ror€(-;1l!J[2;+d); 5) (r - 5X, + 4)(r.'+ 6r + 9) > 0, (r 5)(iu + 4X, + 3)'> 0, , € ( -; 4l u [5; +-) u {-3}. 224- 1 t'(t + lxr - 4) > 0, r € (--; -1) u (4; +-); 2) (a - 3)(r + 2):(r - 5) > 0, r € (--; 3l.u [5; +-). zzs. t1 '',t l- 2l , o. {' al(1i.1 ' u, x'-6-r+9 t,r 3)' re( -; 5)!,(4; +-); t'+t-20 lr-41(r+51 zl -. >0. ->0. ' .r'-6.r+9 (x-3)' x € (--; -51 u [4' +-)' (r+ 3)(r + 6Xt + 5)> 0, x e [-6; -5]u [ 3; +-). t' 4r+5 =0.D=16 20=-4 <0, a iBir- kr.rr rapa6onE HanpaMnelri Bropy, roMy Blrpag r' - 4, + 5 llplti.tM e AoAarHi sEa.reHHfi. 222.1) @ q'z@'- ?r+10)<0, (r - 4)':(r 5Xr: 2) < 0, t e (2; 1l w (4t 5); 2) (r - 4)'(x' 7r + 10) s 0, (tc - 4'(t 5(E - 2J s o, x e 12, 4l v L4t 5l - l2i 5l; ---; /--:- ?--- 7-- --:{- I 21Bx -T,/'-r-?,Z- _-;/_:.2=/-- r i r----.r+ 2tB' --F/-T,,'-:-- ----t---ra-- i r ---Tv--i-.--r,,- + ----1i-i.-i- 1 -t ---Y--/-rr-T, 112,.2 -F)/-'-)/----vTl -4-3Ex 2 , r, / 1 3)(3x 5.r - 2r2x'z x l) 0:3[.r' 6Jtr 2t(2x'-x-1' 0' .rcl-E:2Ji 1,2r'+ r+ 1= 0,, = 1 8 --? < 0, a aBirnr' trapa6onr saEpsMneEi Bropv, roMy trpr .I € -A MsoroqneE 2x' + :c + l rplrllMae AoAarEi 3Ea.reHnfi. 2. 3x' - 5x - 2 = O, D = 25 + 24 = 49, 5 7 1 5+7 -. r^=-=2, '63'6 1 -5 a)(4 r)(3r + 1)(r* + r'z+ 1) < 0. OcRinEKIrJ.'+ 12 +l>O, r€ -R, roaaHaEe- 221.trxa+1)r5 6ir)rx 2'.0: x.[ -,i) -,r,-*,. Bapa3,ra I op'fliMa€ ao.q€rHi rBaqeHHr npx - -?---V. - r € fi, roMy AaHa Hepisqicrr pislocumna Hepin- -i-- -{-, Hocrr (.( sxr 6X.r - 5) > 0. 6 2 G + ak + 6Xr + 5X" - 4r + 5) > 0. 4n HepiBEicr6 piBllocr'I'6lra EepiBnocri ,/'+-/.'//-- -1t--=- a'---! -iz-- -?'-:-_t_t_ _i_____ - i ,,-= /-- ,2-+- -'3---a--r - 3) x'z+x-2O - lx 4Ix+5) - -<u. +<U- .r" 6.r + 9 11 3)' (-5; 3) u (3; 4); x'z+t-2o4t -. <0. r'-6r+S r e l-5; 3) u (3; 4l; --l-,,--=-,,---_---1 13-2 1x'z+2x-1 -4l -zu, a) 3x' + 2r -1 = 0, D = 4+ tZ = rc, t, = ]# = q Axt - x - 4 = 0, D . 1 + 48 = 4e. '- 1:!=t. 8 >0, , e r--; -rru( i, il"o, --,. 22O.1 (2r + 1)(x - 3xr'9 + 4) < 0; 2) 12 - rXSr 5Xr' - ir - I) 0i .r E 3 '/' 'x' - t + 1 = O. D = 1 - 4 = -3 < 0, a (BirIiIt' ra- pa6onu EarpsM,'reHi Bropy, roMy piBsa1lH-t Ee Mae l(opeHis. MBoroqneH.r'z-r - I DpHiMaFroAarHi Bna.reHss np}l t € R. 3l @ a)'@' 7x + !O > O, t e (--; 2) !, (5; +-); 4r(x- 4)'(t'- 7a+10)>0,re (--; 2l u t5; +€) u {4}; 2 1 2-4 = -1: 63',6 1-7 6 3 'aR4 -4 ".( ;,r' ---+-,/- -,/-=_/-+- ----1i--1--a - r)/-),G4 -T-v-:)z=)/T.534r 284 iia; AnTEEPA Mep3ncKA. r. ra iH. AKaaeMieHxr piBer" ii::ilfiili!:l:ii:i ::iril!Jil1.;iit AITEEPA Mep3reKA. r. ra iH. AKaaeMi,{nrai piBeHb ltt 285
  • =-.,,-- ,-' ,/--.-.-!+ 412 E-a€14 1t --aA€412' )/-+-Y---!-r;745_ t:+2t 2 - l-2r+2 ^ ,(j' - 1) ,(' 1) Mroroqner J.j 2r+ 2 nptiiMae aoaarHi 3Ea'relrE.a trpl{t € -R,6oD=4 8 = 4'o i iBirIiI0 napa6ontr y =f 2x + 2 fianpflM'leHi Bropv; xE (0;1)' 286 ::::::: A]nfEEPA Mep3neK A. f. ra iH. AKaAeMi'rHral pieenu :i:i:::i:i;iiiii:ii::i:i:i:i 224.1') (2x + 3)(1 - ar.)a(, - 2)3(r + 6) < 0, x e (--; -6) u (-1,5; 0,25) u (0,25; 2); 2) (1 3r)3(r + 2)?(r + 4)r(,. 3) > 0. /r r.€{--:-4)Lr r3l.il / 3) (rc': + 2r' 15xr.':- 4r -f 3Xx - 1) < 0, (x + sxr 3Xr (.r r. sxr 3)'2(r. 1)i < 0. 2. v=-5,1. r'|t 2r- 15=0: I lJ: r 3i r, r 4, x 3, ..1. x'? 4x+3=0: I 1,, ,. 3, I' r: rc(-;5l',/{1;3}; a) (1 2xxr 3)3(2r + 7)6(jr + 4X, 2)'z> 0, /r l r. €1--: - 4)!I t| 2] u (2i 3). 229. 1) (3 r)3(r + 2)r{x 1)(2x 5).- 0, jr € (1; 2,5) Lr (3; +-); 2) (r: a)(ri + r 2) < 0, (x 2')(x + 2(x + 2)(r r) < 0, - x 2-t I lr lr lx l') 0.br , '2, 8 (r 2r(i | 4r' r'' 2nr I ll a E (--; 4) u (2i +-)i n, I 2"+1-n- lx-ll': -0,- .r' + 2:r 8 (x 2)(r. + a) re(-;4)u(2;-r*)',11); -r r-,2.x+1<0. t" lt _0.'' r'|+21 8 (jr-2Xx+4) ,x€(.1;1),J(1;2)j R, r ?{lr. o. lt lL.0.- x +2r I (r.-2)({+4) r. € ( 4; 1l L, 11; 2) = { a; 2). 226.t, x 2 3:t t 4 , t! Zl (3" 4) 0. f,+3 x+3 x+3 21 2 o.2tx-r'n,, 1 1,,.r_( J:tl: r+3 r+3 .j.+3 2) t'*3i: 28', f, +3jr 28-0. xb i. 4t(.r,;) u. r_l?;41 L;:,_lr r5 rl 1. r, 1-I. o, ir € (-*; O) u (1; +-); I 1 2x-r 3 ^ x-3 o' ' -, , -r,r-ri o r;; ;, o i. e (--; 3) u (3; +-); r € ( -; 1) u (0; 0,5) u (1; +-). 7,2_ | .1, 2(n lr '_1,, tt.O. .{ I I r(/-r, r€(*;2)u[1;+*);] 1 L22. '-2(r'+l)-0.r+l x+l .re[2;-1); .,1 5'1!.2, 7'+8 2G !.0, 1a4x xE(-j0)u(4;+-); x-2x-2 x 2 r+2>0. :0. <0. r+1 r+1 r+1 5r+8 8+21 7r .0_ < {l- 4-r 4 t --GA4 4,5-23' 227. tt I r. I (r 2) o. l--'.2 o. ' I o. '-l .o- x 2 ,,2 r,2 r.2 x-2 1111111l .!!!!!!:4Il ir::::::::::::1$ 31 ,, 2 , 1 2(x-1, ir+3) .n' j+3 .ir 1 (x+3r(x 1) '' .. e ( 3; 1) u 15; +-). (jr - 2)(r + 2)'9(r. - 1) < 0, x € I1i 2lJ 2j: 3) (ir3 ar)(ir'? + 21 8xjr'?+ Ijr + 10) < 0, xlx zlx + 2)O + ax 2)(r + 2xjr + 5) < 0, x(x 2'(x + 2)'(r + 4X, + 5) < 0, x€( -; slL]t a; 0lLr{2}. 23o. r, 4l !11'1!l , o. (x 8XI 4t) /r t€r 5i 0) u lt; 1l ,-r(1t8lr 2t t' 2{?!l!, o. (3 r)'(1 sr)' I tt lt r I€l -; lul r,l: :::::::ii::iiii*i: AnTEEPA Mep3nqK a. 2x2x} 15> 1,. -- : tl. (.r + 3Xr 1) (x + 3)(r t) ?-T/- 7' /-+ 631, ti 5 + 3Xr. + 1Xr 1) < 0; )/G)t--.)/-r , 513n ., I 3- x-3, 3rr. 2i-0. r 3-3r 6 0, 2- 9-.0. "'x'2 x 3 (r. 2)(J-3) lr 2){t 3) tr'ztt:t tt -2(j.+1,5) <0, (t+2/'-3 r € ( 4,5; 2) '.r (3; +-)i 0,,_l ,_ I Z, lr-l|n! ll ,1..1ll 2irlir l) o. xl x(' l) r." 2x+1 '"'-r' 2r'!+2x <o, ,41: jrl!<0, 1"trJl;.o, :,l](x 1) 2a" + x-7 >o. 2x!'t r 1=o,r=1 +8=9, r(r 1) ,1 3 -1+3 2 1 t *"= n =l=t' - +--7-:,,-_,/-+ /-l /- 4 ,12 -*--d-lt-,1r1 -2 12,5 3ir +)/--+/- --)/-1 - 272l. --Y-.')/--Y-)/-r)1 , 5 2 -1 011 2 2x 2-r x'+r >O, r(x -I) 011 4 1123 ti +/' ,-f?- z- f. ra iH. AKaAeMi.rHLah pis'e{b tiii.. 287
  • n, ,'la' llg + zt =o, st !- :ya' - 11.. o, , . [- 9, - z] - t,r, , *r, (x-3")(x+1)' L 4 l - /.= /.= /_;,,---dIIa- -1 _i_4 )AAOG30l2t = (:; 3) !, [o; 2); 5 ^ (jr 6)3(,r - 4x6 - .rtrj) - -, >0. ,r+5t r€ (--j 6l!t 4;61. rii,iifiiiili lli.;i!ili.:i-ii z3r . rv t* - "'*^ .'-r . o. i, ltl;: .:.:i.i:.:* l.n - itl ;;:,!tj::d..i!itj x. [l:21 .r[2:3)=[ri 3r: ililf::;i"t+li 2r rx-1)'?{x+2)3 >0. ,iilii-::.!1:ri!t Y , 5 'i::,--::.i::::::ii.:: r._ t _t 2, . (5: _-)u{11: 3t !'lt' ll . o. 'r'?lJ' - I,(r' - U , 0. r 4 x-4 .r € (-1; 0) u (0; 1) u (4; +-); {r l)':{t 2)'t'Y 3}i < 0,4'_-- J' e (0; 1l u [1; 2] u {3} = (o; 2l u {3}. z1 1r'-g,["" nrO. tvtu"*o 1[La'0, sliqo r € ( -; -2) u (2; +-) -3Eari Aanoi HepiBHocri sen€nirrr, BiA sEaxa Brrpasy .r2 - 1, rorry r, - 1 > 0, (x lxju + 1) > 0, sRqo r € (--; -1) u (1; +-). I]eperEEoM aBox MHo]r{Ilrr € Mrro- ]]{lxrar€ ( -: 2)e(2:+*, BiAnoqiAb: t. ( -; 2) u (2; +*). :1 1r'-rluft 7<O, posB'ssnoM e.r=12. Bdnoeidb: x . !2. 4) (r'z -1)rV 4 > o, posB'ssnoM e Muo,rcr.rEa ( -; 2l !, [2; +-). BiAno6i6b: te ( -; 2lu[2;+6) S1 1r" - Sr+qu7 lt*tO<0. Snan sapaay .,tt:t;lo aoaar''i Ha Mso rlr*i l,I -( -:2v(5t -). royy AaHa HepiEEicrb Bn- KoHy€rbcs. rRrlo (-r? 5r. 4, 0 Ha MEoxfisi M. Orrfte. lx 4X.r I ) 0i r. e (1i 4r. SHafiaeMo nepernH MHoxrrs M i M (lt 4). -v e (1: 2). BiAnosiAb: t€ (1;2). t7 1"" - t, + t1..,Q 7a11s,s. r€(-; 2)u(5j+-). -65 4 ,,?,,-T.?'=-/-- +/'= /z /=/1- 3--i---t-1--- 233.1) ?E:j) < 1:, 2G - 3)(' 1)-{'-6)<o, r(x-6)('-t) tQe 6)(r -1 t'z-2r+6< {)_ < {). /(' 6XJ. - 1) MnoroqneE r' - 2, + 6 npd;Mae AoAarni sHa.relrss, roMy sHa& Aalroro Apo6y sa"'re: ){rrrr, BiA sHaKa sllareEExfta, , € ( -; 0) -] (1; 6); 2a-3 1 2t2xt3t rx'/,x -t2l 2i"t'+x-12 2 !'+x 12 r:+3:r+18 - -{,!"-Jr-18) - -<u. <u. tr + 4)(jr 3) (.r + 4X.r - 3) x+12 <0, (r+4)(r-3) --T,,--,4,/- ,r-- -4-336t 1"-6lI+,0. r - ( -i 4) ( 3i B) ,(6: --).(.r + 4)("r 3) zs4. ti @' -JV - +. o, (* rxr + r)uG zX,+a<o. 3sa,{eHHr srpary rr:4 ic}rrr.nrcuox' a-0. ,--/'-=-/- ro6ro Ans r e (-*; -21 u [2; +-), ane aana l{e- t--- -- piBHicl! He npper6a'rac piBHrcr6 Hyiro, rovy ir po3B'ssxr yKarlrMeMo Es MEoxIrHi ( -; 2) u (2; +-), Ae 3II"*"""o f,L A t O, roAi snari AaHoi HepiBHocri Bane)&arlrMe BiA BsaRa Blrpasy (t- f)(r + 1). --- +------- -- ---1i -i - --+--,--=-zT ------i-i --- SEan Brpasy Jl-?r.10 aoaarnri, ssrqo Ba yMoBn (r2 - 5r + 4) > 0, 1:-:;!i+zyr-n>0, *.,:, tt.,,fo, ll.,[], r'l L UI tU ,/ -1 AaHa HepiBHicr6 BsrcoHy€rr.cs Ha rlii MEorr(sEi (r 1X, - 4) > 0, snrqo r e (--; 1) u (4; +-). 3HafiAeMo treperrH MrrorlnE: ir e (-*; 1) u (5 +-). BiAnogiAb: t e (--; 1) u (5; +-). z) (tc" -rx + +r.[x" lt+ to< 0,, € t1; 2] u {5}; e @" Sr++Jr' -Zx+tO ) 0, .r e ( -; 1l u t5; +-) u {2}. "-' x(z-6)- t 1' 2z'-6x-2x+6-x'+6r 235, 1) (, - s){4 + 5r - ''z > 0, jr e (3; ?). -x2 + 5x + 14 = O, t' - 5x 14= O, ,=25+56=81, 5+9 5-9- I 7. ,t z - -2. Ha usoNntti (-2i 7) uryxaruMeMo po3B fl3xn nanoi EepiBHocri. 3a yMoBoro MaeMo: jr 3 > 0, r > 3. BiAnoBiAb: zE (3;7r. 2, (, - 3rJt4 + 5, - "" > O, o!:s. , e [-2i 71. BiAnosiAb: ': € f3; 7l r., {-2}, -- 7. X--- 29z' -----a21) )'7-7v'--. 2-/A7' t.' - sttx + srfa - x1a -'1 . o.u/i+ *rre xt 'o --,..+t,--_ Ea MEor{rEi ( 4; 4), roAi Arf, BlIroEaEE.a AaEoi -------------- + EepiBgocri troBr.rH'a Brr.orryBar"J;;;l;;l; -4 4 x x' 25. o.lx 5)(-! 5) 0. r. c (-5: 5). 3safi. - --:-- | AeMo reperr.,E Maolrcr*: r e ( 4i 4. ----1i':"": ---- BiAnosiAb:te(4;4). iii:ilillttilii: AnTEEPA Mep3rsK A. r. ra iH. AxaaeMiqHrn piBeHb i{t 2a9 l0 Yci rnP, lou.,r.l al (r - s).,,/ia + 5" - '' <0, sxrlo .r 3<o,r<3 Ha MEoxcnEi (-2; 7), 10610.' € ( 2; 3). BiAnoqiAb: re ( 2t3. 4, (, -3r^114+5, - '" <0, srcqof,-3<0,r<J Ea MEo,{rI{i [ 2t 71, ro6ro r < t-2t 3] u {'Il. Bidno4iAb: r e t 2;31 u{7}. st @" - zlJta - ,' <o, UIo6 6yrTa BqRoHaEa yMoBa, rorpi6Ho po3B'fisarx IIepiBHicrE (, 1)(r + 1) < 0, x e (-1j 1). 3Ha;AeEa MHo'lrrria IIe rlan${Ifr6 MI{or{I[d (--; -2) u (2; +-l rovy aala scpiBHicrb Hc Mac porB'rrtsiB. BiAno6idb: E.piBl{lcrh He Ma. porB arKrs. z8s itjl! ArrEEpA Mep3rrK A. r. ra iH. AKaaeMieHrt piBexr tlililllllilitli!
  • o) (r' zs).,/io - '' '0, '"pu" .,/io - '" 'oHa MHo)n si ( 4: 4). lqo6 46Ha HepiBHicrb BU- xoqysria.F. troBfiHHa BHKoH) sartrc't HFpiBuiclb (x 5(r + 5) > 0, ,. € ( *; 5) ., (5; +-) BEa;- AFMo nepprlrH A. AaHa sepiBHicrb He Biano8iAb. pos3'ssftiB EeMae. r @" zli|Jta - ," < 0. Aalra EepiBHicrb BnrloHy€r6cs, sKqo 16 ,' > 0 na MHo- rc'Eil4; 41,"G'-25)<O,(x 5)(x. + 5)<0,jrc[ 5; 5]. SHaiiaeMo reperrE MIIonitrE: , E [ 4; 41. .[aHa EepiBnicrb Brriolly€rbcn, srcqo t e [-4; 4]. BionosiAb:tel4t4l. ay 1r' :r).,/ia-l <0. PocB"rsIloM AaHoi EepiBtsocri !5al4i4l. 236. -L s -L.x'-9 r" I +4, 60 +4 € [-4j 4], a 3Ha.reHHfl ," gt t" -g' -{ .o- --+- _-.',-'+. 5- ---zs x .-, -a--a5-445x :--/-+-7--r--/-- ti---t- 1 BnpaBl,l Ar9 noaropeHHt 1' r:f ::':.:.:.:.1:.:: 10-2x !t= 5 4 " =9 '' e, +zs = 61 -6-3rt, , '. ]*' e-''-e'uooz. ln:=o' Po3B'fir{eMo c creMy: [.' -,' .0. 19".0. r, l.r'-e .r' e lx'-e l=:."' l=:'o' r. € ( 3; 0l .r (3; +-); 24O. 1) lv ,' =,, I2x+5s=ro: t " ' lzx ,, ]'' s "'-n=u ]t n'u,_r. -j-. o, i-5. o: tr.'-g |,r'-s Bi1nMiAb: t3.01 u (3; +-). . lI-1 -o. [ll.o. "-.1+1.,:-:u' l',,-iu r,,-, j1",',' x t 1,, ro - *^ _ rs, 1,, _ ro. ,. lo. I r-1- .o, Po3B's)+rFMo rr.{r'reMv r,f, ]*"u x - ( 4i Il' (4: --). llr ; 'o o' I r-1 -- -0, P..'R excMo.r.reMv r2r' ]'' I6 x ,.. '"^ 1'o:r? - 16 Bilnosilb: (4;11 u (4; +-). 290 ai{: ATTEEPA Mep3neKA. r. ra iH. AKaaeMi'aHxi piBexr {iii:lliil:iiilti BiAno6i0b: 2 napv. (r; U) | G,: v). l6 241- u=1 x lr',snqor'-t. BiAnMiAb: qy'lr{nr 3pocrae Ea npoMir{Liax ( -; 1l u [0; +*); Oyslrqis cnaAae na npo Mir*xy ( 1; 01. BiAnosiAb: crrcre!a Ee Mae :il::iJtiilitiai ATTEEPA Mep3reK A. r. ra iH. AKaaeMi,{Hui piBeHb i::]i 291 l0* BiAnosiAb: x=-1, a=3- BiAno1iAb: , = 2.
  • s3. cTEnEHEBA OvHKqlC 1. CTeneHeBa OyHxqit 3 HayypanbHirM noKasHt(oM 242. v = i6. Toql(a B(2; 32) Eate'Iirrb rpaoiRv OvErcqii v = t5; roclca D ( 3; -243) Irane){r{rE rpaoiEy oyEnqii y = ,i. / r r) 243, rpaoiK QyFrqii y = .r' rpoxoau rb sepe3 roqKn: A(2: I 6)r Cl - i: -8 t.J. _12 _3 244.A12i -12)t t2=a 2t. a , i;.r= ;. 3 ncn a - - i rpa+iK Svsxrii v = axa opoxoanrb sepe3 roqKv,{. '" '-st'= a'B(-8i 3): -3 = a (-3)', a = -. = (-3) 27 1 nor a ' -fi rpa$ix (DyHHaii Dpoxo4 r!, 'repe3 roqRv B. _1a 2 245. C(3: 18): 18 = a 33; a 3- 3. g: = J fipri a = -: rpaoilt SyH$qii y = ai3 trpoxoAxrh qep€ roqnv C. 64 DF2;64:64-a (-2)", a _-=-8. tlpu a = -8 rpaoiK O],slcEii y = af npoxoar'rrr, 'Iepe3 roq}tv D. 246, f(xt = x's, 1) f(1,4) < l(1,s); 2) f( 7,6, > l(-8,5):3) l(-6,9) < l(6,9); 4, f(o'z)'> f(-12' 247-ftx)=x. 1) l(20) > l(1?); 2) feaa, < f(1,5',3t f(-52 < f( 45',. 24a. ^x, = x'zo. 1) t(s,6) < l(4,2); 2) l(-6,7) > t(-5,8); 3t f(-2,4, = f(2,4t 4 f(-15) > ^2. 249. l(x) = r{. 1) l(9,2) > l(8,5); 2 f(-t,I, < 1( 1,2i 3) (1e) = l(-1e); 4 f(-7) < f(s). iso. '" = 1600. 1) n - trapEe LarypaiEEe qlncnoi aBa riopess; 2) n - EerapHe sarypanr'Ee cltcno: oanB KopiEl,. .82 251.1) 's = 32. r = 5i 2 t' . -;7, x = -il 3) 'i =81; t=13; 4, ,.a=-16: xe O. 252, 1) tx = -27 , r = -3; 2) t' = 0,00032' x - O,2; 3) xo = 64, t = !2t 4 13 = -l' reA. 253.1) 16 = 2, rarci 2) .'5 = -3, rali; 3) t? = I, Ei; 4) t6 = -10' IIi. ,s4.[ ;J', i-?]', t ll', (-fJ' 255. (-0,48){i (1,06)'i e2,12)a', ( 3,25t4. 292 iili anrEEPA Mep3reK A. r. ra iH. AKaaeMi,{Hur piaeau i:3i1*ili:iJlit 256. r a = f iy.=zxa; x6 = 2a4, a1(z' 2-o,x-o,,=-"E, ,="E; a =o,a = I, y = 8; (o; o); f"E; s); (.8; s). 2l U = ra i A = -27xi xa = 27x, a = o, t = -3: a = 81i (0; 0); (-3; 257. y = x6 i y = f , ri = ts, x3(z' - a,= O, a"= 1, ys = 1; (0; 0); (1; t(x3 + 27)=0, t(x+ 3)(r' 3, + 9) - 0,, = 0, 81). t) = 0: r3(,r - lr(r + l) =0. r =0. r = l. r = -1: 1); ( 1; 1). 258.1)a=x3-1i 3) a = -t"; 5)y=(x-1)ai 2a=@+ 4)v=ra 4; er,= 1''"2 3 iiiiitlillllili AITEEPA Mep3rrl( A. r. ra iH. AKaAeMi,{Hr4t piBeHb :iiii 293
  • lit! ::4.'ii:.ii:: ' tit;ria!!i:.! 259.1a=t3+3i 2y-(x-3)3i 3)a=rn+2i 4)a=G+1): t"5 Y= x', 6a= xn' 260, 1) l(.!) = r's, js e [0; 2]. Ha rrBoMy npoMi,r.fty {DyErirris spocra€, roMv EafiMesIIIe slla.rellHn Bolra np[IiMae, nriu{o, = 0, ro6ro 03 = 0, a Hafi6in]'ue - qtrqo t = 2' ro6ro 23 = 2a 2a = 16 . 16 = 256. 2) t e f 2i 11. Ha qboMy npoMix(y OyHxIriE cna.4ae, roMy san6irLrre sHa.reHIIn Bosa nplriiMae, sKrqo t = 2, ro6ro (-2)3 = 256, a nailMeErre 3HaqeElis nKulo r = 1, ro6ro 13 = 1. 3) ' e [-1; 1]. .fl{rqo jl: = 0, ro OyEtcr{in rpl,liMa€ HaiMeEde sHaqeHss' 03 = 0' sknroJ' = 11, ro &ys!{qis rpriiMa€ Haii6irLre sHaqeIIHs, ro6ro ( 1f = 1a = l' 60 sa rpoMixcxy [-1j 0] Bosa cnaAae, a Ea rpoMi]cRy [0; 1l - 3pocrae. 4) (-*; 2l. Ha qboMy rpoMirri(y &yllrlllis craAae, sail6ijIblne rr rre MornHa, a HaiiMeHlrre 3HarreEEs oyllRqif rprfiMae, sntqo x ='2' ao6'to r 2)3 - 256. 261,1)f(rr=t5,re t 3; 31. Ha qboMy npoMi}}{ny OyExuiF 3pocra€, roMy Ea;6inblne 3HaqeHnn rpriMae, sxrqo t = 3, ro6ro 35 = 243, a HaiiMeErre 3t{a'{eHEn nlcqo r = 3, ro6ro ( 3)i = 243. 2) [ 2; 0]. Ha qboMy rlpoMiJrtl(y OynRrlis 3pocra€, roMy Hafi6inbl$e 3Eaqet{Hs tbvH- Kris np iiMae, nriqo t = 0, ro6ro 05= 0, a EaIiMeIr e 3HaqeEEn $11o r'-2, 10610 ( 2)'. -32. 3) [1; t--). @ytsl(llis Bpocra€, EaiiMeEsie sHaqeEHn trpriiMa€, sR[Io r = 1, ro6ro 1r = 1. a Hai6inB]le 3Ea.IeHEn BKa3arrr He Mor(Ea. 262.1 t3= r + 1- aBa 2)x5=3-2x oarrE 3)/=0,5r. 2 - ]Koa- Ilopesi; lcopiHb; Irorc $opeEn. 266'.1 xt' = a 6. y = r" - lpaoilr qiei OynKlrii cnMerpltqErn BianocHo oci Oy, y > 0. a = a - 6 - rpaoiRoM qiei OyEliqii e rp€Ma, Ena npoxoavrb 'repe3 ro'rKv (0; 6). flRrqo (, - 6 > 0, ro6ro a > 6, ro pisH.nHH.n Mae aBa lropesi; sr{qo d - 6 = 0, ro6ro a = 6, ro piBEsHEn Ma€ oAIrIr RopiEb; .slirqo d - 6 < 0, ro6ro lr < 6, ro piBEsEHs Ee Mae KopeHiB. BiAnoqiAb: 1) a > 6, aBa l(oped; 2) d = 6, oar'tH nopiE6; 3) a < 6, xtoaHoro rcopeHn. 2)'^=a,+7a-8(1), a = *4 ryaOiK qiei Oylllcqii crMerpt'rErn BiaEocHo ocl O!, ! > O. tbrrJoa'+7a 8=0, roa= 8, d= 1, roAi piBEsHrIn (1)Ms€ oAtlr EopiEI';.sHrqo a2 +7a I > 0, ro6rod€ ( *; 8)u(1; +-), ro piBHnsHs (f) Ma€ aBa lloperii; sllqoo'+ 7 8 <0,ro6rod€ ( 8; 1), ro piBEsIrEn (1) He Ma€ EopeEiB. Bionosi.Ab: tt:1"no (r € (-8i 1), ro piB1rnlrHs IIe Ma€ KopeHiB; nKqo a € { 8; 1}, ro piBEnHHE Ma€ oAlr]i RopiHb; nErqo o € ( -; 8) u (1; +-), ro piB}].'sH.t Mae ABa lcopeEi. 267 - ts = 9a a3 (l). rpaoni Oysr{qii y - '3 caMerb@sr; gi{lloc:do oci Oa, a > O. fiKqosa a3=0,ro6roa(9 a'z)=0,4(3 aX9+a)=0, a=0, a= 3ia=3,1o piBE.'riIIr (1) Mae oar.rE llopitlB. i;;iiJiltiil!!! AnreSPA Mep3rqK A. r. ra iH. AKaaeMi,{Br'ti piBeBb ::i::: 295 26s. Iv = '"' l2x-s-3=o; a=2x-3; ,{oanoro KopeEF. Ha IlpoMirftI(y ( -; 0) OyHKrriE craaa€, a Ha rlpoM { cy [0; +-) Bpocra€. [x'.sxuox.o. 265- tQ)= _ ./r. nxxro ir > U. na ,'poori*rry (--i 0) OyE(- qis spocrae, a Ha npoMi*rEy [0; +*) cnanae. ,, r,,, {r" axuo r ' -r' I r 2. '*nro x: 1. Ha npo}tiniKy (--; -1) OyH Iis spocra€, a Ira rpoMi){Ky [-1; +€) cna,qae. I:r'.sxuor<0. /(r) = I -lJr.rxqor>0. 294 l::i AITEEPA Mep3reK A. r. ra iH. AKaAeMi,{Hrar pieeHu illlii-:::::il:!ii:l
  • gKqo 9a - 03 > 0, ro 4(3 - a)(3 + a) > 0, ro6ro a e (--; -3) u (0i 3), roai piB- EsEIls (1) Mae ABa KopeEi. fiRrqo 9a - a3 < 0, ro a e (-3; 0) u (3; +-), roai piBHsHns (1) Ee Ma€ I{opeHiB. Bianosiqb: ttKLro a e (-3; 0) u (3; +*), ro piBHrHEr Ee Ma€ xoAHoro nopess; Elcqo ae (--; -3) u (0; 3), ro piBEsEEs Mae aBa riopeEi; sRqo a = -3, a=0, a=3,ro piBEsIIlIs Ma€ oAnH (opiH6. 264. f@J = x^. 1 tC4') > f(-21, r, - rapHrrfi noKa3rrnK; 2) f(-4) < f(2), /, - HenapErdi noKa3slrr{; 3 f(-4) < f(-2, n - senapgr{ia ronasH*rx; 4 IAI J(2,, - Mo)ne 6yr,.r i napH M, i HenapEuM, 5) f(-4j > f(21, n - napHr.rii nol{a3Er.rli; 6') f(41> f(-2, /, - Moxce 6yur dapll rM i H€rapFrM, .r' =( ;)' =* rpaoi* se rpoxoa'rrE.repes ro.{xvB; (i)" = * = rt rpaabi& npoxoat rE.repes roqfty c; . {Jr) -li-l =i. rn.oi* He npoxoruflr sepe3 rocK} D. 273. r)-a(o; 0), 0 5 - 0. Br.rpas IIe Ma€ BMicry, rpaabilr lle rpoxoalrrL qep€3 ro.rRy-4(o; 0); 2) B( 1; 1), (-1)-' = -r. fpaibiK npoxoarrb qepe3 ro'Dcv B( 1; 1); :r cf |, ezJ. lli = r' = n. rpsoilr trpoxoarrb qep* -"*y c( 1, 32 l, ar al -s,---L1., sr' I tl'-- t 243) t 3' 243 fpa(bix npoxoArrh qepes roqfty D[-3: - 24A-J. 274.y=aat, 1) A(-5; 20), 20 = @ . ( 5)-s; ", t(r'l-). L = ".2'. 24) 24 275. y = 6t. t o -3t l: a=-2q.a:I)A(3: -3): -3=a 3{t 3 d 3.r 8I ,, r( -",11. 1. = o . r-2 , . , = I , I - I l' - I , r .s.' '2) 2 2 2) 2 t6 1 276. f(rt = x ", flxt = :n,. 1) fl1,6) > flz); 2) f(-5,6) < f( 6,5); 3) {-e,6) < fls,6); 4) l(0,1) > l(-10). I 277.f(xr=r". fr = ,*. 1) l(18) < l(16); 2l f|a,z < f(2,5)t 3) l( 32) > l( 28). t 27A. fU) = x ''. flrt = --:. 1) f(1,61> f(2,21; 2) fta,6l < fl-3,6tt 3) l( 3,4) = l(3,4); 4) l(-18) < l(3). 1 275. J(xl = x 1o, flx, . xao. 1) t(6,2) < l(5,5); 2) l(-1,6) > f(-1,7t 3) f(24 - f( 2a); a) fl 8) < t(6). 11 280. x'= 2500; " 2500r r'= r5_. 7l n trapse tsarypanbge {rcno. com} pisssHlrs x' - -l ** ouu nop"ti; 2) , - Eeilspse HarypaibEe .rrcno, roMy piB """rs ,' = ,h Ma€ oarH Kopixb. rl{ltil::tl:ij::: AITEEPA Mep3nqKA. r. ra iH. AKaseMi'{Hr,rr piEeHb iii: 297 "(', *)' "l.1, rtl. t3 ) "@'i) .frtii:il:::Ja-:::i: :t;lI'lAi-:J..'1.', liii:ra:t::::i!:i: rj :ti;Ar'.' ' ry 'u'. 'r " =(])", ' "^=(:)"' foryeMocs ao BrBgeHHr HoaoiTeM, , *=(;)" a) a- s1 n'=l; 6) -' /ll - l;,r ' 1 / 3rL =- z) 51 0.5,.4, = l1l-'.1= 4.1= 1. 2J44 6r r2.,-s ,.16r, = I 1- !. rel '_ I t -rl ' t2 8 ) 2 ) i_rr*i lr.t.:.{1 z 1a-01" =--J- q (2x-3! a = 1 lo-b)' "' (2x -3!J)' zzo.r ar 4'-1 1=4-3= 1: 3412 12 !- I 9t? !!. 8367272 :r l2l', rz.sf s, 7,r r _ t75+50- 2. =?23 -a2?. 7) 2 25 50 50 50 4.)9 0,1 .9 r0 goi =l-,11'2) 2 3 271.It a'z+d '=1-1=S+, 2t nn-rn ,,i 3)r., d,)r. ,,,_f' ll t __ d.c _ t . I c d)(e d't'- .d(c d)'z (d c)td' "., (t r') I s2+x' I 1 4l (x -u llx -u ) =l-+-1.-r' u)r-c" x!2 xz-a'? x'/ 2. CTeneHeBa OyHKqie 3 qi,|rM noKa3H]'KoM 272. a = xa e [:, ,'u.1. z . I j l' ,'u. .0"o,* npoxon,'rL qepe3 roqky A; 296 iii: AITEEPA Mep3reK A. r. ra iH. AKaAeMi.rHr,ri piBeHb ii:.:iii::iii:{i:jj 26=--L. o=-25691 125 la1 24 R'' 3
  • ii$i#$ii'l{l ;A:::::::l 'iiIijfiiiri itirljft:iii ttr'2a1.tt!=tx 't'., LJ - u=x.r'o O6nacrB BE3na.reIIHs {ryHKaii qe r(y) = (-*; 0) u (oj +-). 2) u = ttx - zt"t'., =l - !-l tx-zt ) t 2+0, r.+2,a=(k 2r')',A=G -2r4, D(a) = ( 12) u (2; +-). 282.1t r' z. l. z. ,, o.Toai ro I 11 x"2 ra', piBEEHr' r d= 2 Ma€ BiAtMErn r{opiHb, r=-i/!. r 3 to iro 2r -r' 0.3. " = 10, ' 0. To4i x'= S , r, i: . Hi, piBHnHHn r. 5 = 0,3 re Mae BiA'eMHoro IropeHs. 2€.4.a x" i u=.1x. gxqo rpa,liKx d,yHXqria nepelrHdlor!'.s. ro BHKoHycrb.fl prB nicrs: ra l'. l=1.,.o.32 1" 0. x"=32.r' 2. 32 t' 32 32r' r** **-"* fr, 11.- I 16'r 285.1)g=x'+2. D(. = ( *i 0) u (0; +*). 2)y=(r 3)'. D(fi = (. *; 3) u (3; +-). 1 ' tx 3f' 1" 2 ,(/l = ( -; 0) u (0; +-), 1 11 3tx-=-3, ", t -,0.ToAi -'.3i,y TdK, pisFaHHF j ; 3 Md. Bin'cvprt kopi'rL. /r !a rl i/- ir !B 4txs--2. )^ z,,, o.Toai x'=-.1 t qs prBl{rcrb He BI'IKoIlv€rrcs, oo JIlBa qacruEa AoAarna, a npaBa - BiA'€Msa. Hi, piBEsstl.s r 3 = 2 He Ma€ Bi.q'€MEoro ftopell.fl. 2ag, I a = x, ryaoinoM € trpsMa, sKa € 6ice(' rpncorc I i III noopalrHarHr'x riyri!. 1 y=x3.flnqox+0.ro y=-. Toq&r nepersl]y .paoilliB: (1; 1) i ( 1; 1). 1 II cnoci6: x= r 3: r==. x+0r T=0,,,,=1,n=11. MaeMo ro.r(r: (-1; -1) i (1; 1). 1 2) i/ =,r'?. flr{u{o r + 0, ao u = 1 rIu = 8, rpaQrk qr.r qryHKUll - npFva. .filga rpoxoArr6 qepes roql{y (0; 0). / 11 ro.rKa neperrHy rpaoiKjB: { 2r ]. .l1r II cnoci6: x. = rr , = a. .r * Ui : j =0.:r'=s,x=2. r*'. -*', lr, 1) " tl 5)y=(, 1) 3,D(R=(--; 1)u(1; +-), 1 6) a = tt", D(f) = ( *;0) , (0; +-), l 4)s='3 1.r(1,=( -i0),(0:+-), ' (.r - 1)" 298 iji AITEEPA Mep3rcK A. r. ra iH. AKaaeMi,{Hlln piBelh l::itl::liltlil:i iiiliitiiiiilt! AIrEEPA Mep3reKA. r. ra iH. AKaaeMi,{Hrai pieexe illi zss
  • 2)a=415,x+Oi 289. 1) CrcreMa Mae qorrp'r rapr pGB's3rciB. 290. 1) 2t l!=* [''r'=''2s2. f(x= 1-.r-"-1<1s 1; l-!",x>1. (F}'Irrqis cra,qa€ Ea rpoMilriKax: (--; -11; [0; 1]; (1; +-). OyEXais spocrae Ha npoMi}Irlly [-1; 01. 1"8 1 287./t.rt=xb.RkuoxtO.'to l(xt= a. npaoiK OlBKuii cltMPrpxqHxri BinBocso oci l' l Oy. Ha trpoMi)Rlty jr 1J rlaoix Qverculi cna,qa€, roMy naii6inr,Ee 3Ea"eEns abvH- | - 'l I' ltu ^" -'xqin Ha6yBa.. nxsro r = 2. ro0ro /[tJ = | z) . r' = on. savMeslDoro 3HaqeBs' abyHrcqiE Ea6yBa€, ff{rqo r = 1, "0610 l(1) = 1. Ha npoMi*c(y lt, - |l Ou'^*'" rpocrac. rox,ry sanMexne 3HaqeEH': /(-1) = li -/ rl / 1l Es*6inhme 3HaqeHHn: f, ;) ,-;) =( 2t6 64. Ha rpoMixir{y [1i +*) ibytrKqin cfla{a€, roMy lrafi6inblt€ sssqenHs: l(1) = 1' a safi- Mesmoro sHaqeHss OyEKqis He Ha6yBae. 288. f(x) = t3. lr 1 1 I) Ha npoMilxnv l;;zl Ovxxnin /(x)- -" cna-aac. roMv 'rafi6i,bore 3sa'renss ,(! "' ,r., .'u*"-" ""'""", I I '3/ sa ltzt= '' I 2) Ha rpoMixclcy t 2; 1l Oygrrqin /ttt = I "ou*"", roMy Hai6inlrte 3na'reEs.E ft z 1._=-1. " rrn.a""-e sEaqeHsn: 11 11- f= 1. ' (-2)' 8 (-1) 3) Ha npoMinrxy {--; -31 Oyrxqig l(rt = 1 cna.qae roMv Hafi6inbr',roro 3Ha'{eHEs BoHa tse Ha6yBac. a Ha;MeHUe rtse*e'nr, t, 3) . (-1," = +. CrcreMa Ma€ rplj napn poBB'ssRiB. lr '- srrno r < -r-291. l(.r)=l - L-r'. sR'-qo ,r > -r. (DyA&qia Bpocra€, sriqo J. e (--; -11, , € [0; +-). OylrRqi.n cna,qae, .fiKqo r€( 1;01. 3) y=(r+1a CEcreMe Ma€ aBi IIapIl po3B'sa1ciB, C*qreMa Mae aBi fiapa po3B's3&is. 1 300 l::::: At'tTEEPA MepsnrK A, r. ra iH. AxaaeMiqgri piBeHh l:iliii{i:iiil;itl [.atgi:1i.:llli AITEEPA Mep3reKA. r. ra iH. AKaseMi.{Hrn pi8eHb il{: 3O1
  • q rl ti :::a;il* ii;;,fl :li:l:.fl il I I l'- l' ". [0;9) u (9; +-) lr>Ui T 2gg. x) = t', ro6ro npu r * 0, l(r) = 1 t) f(-2 < f( 1), roai n - HenapEe qvcnoi 2) f(-2 < f(1, roai r - Br3Haqltrr seMor{inz Bo; 3) fl-2 < fl-L), aonj, n - napEe qncno; a) l(2) < l(1), roai n alrsHacrru EeMor*{,rsao. foryeMoca ao BxB,{eHBt HoBoiteMtr 2s4- 1 514 - lr5 = 5.2,5 = 5: z, 1.6.0s z=! o.a z= r,gr a) (.,/L)' 3('6)'=18 3 8=13-24=-11; +, 1{,,/is) 'rJrn) - t..ta | .rn "-rr= ".6262 295.1x'=25ix=!5; 2) t'=O,49t r=1O,7; 3)rr=3;r=tJ3; 4) x.'= -25,,j' € A (a6o I:e Mae AincE]rx xopeHiB), 296. 1) J :r, qefi lupas Mae 3Micr, nlllqo .1.>0,ro6rot<0,.1€ ( -; 01. 2) r,F, qefi srpag uae 3Micr, nrrqo t € R. 3) J r', qefi sr{pag -ae 3Micr, nnrqo -r'z> O, t: < 0, ro6ro t = 0. a) Jx-8, aefi B1Ipa5 Mae 3Micr, n&Ijlo t 8>0,ro6ror>8, 1e [8i+-). q JVi, qe* Bllpa3 Mae 3Micr rp't x € ,R, 60.r':? o i I > 0, roMv ixnn cvMa 6in6ua BiA Hyn'. 6) 1G - sf, qeil Bqpa3 Ma€ 3Micr, srtnro ' e ,R. ll - | , qei BHpar MaF 3vicr trpx ). . 8. 106,0 'r {-@: 8l {8: ' €) Jrn 8)' 8l i , qer snpas Ma€ 3Micr, f"f a*0, ["G*s. ' lr>0: [x>0r 297. 1) TaE; 2) rax; 3) ra&i 4) Hi; 5) ran; 6) tsi. 2ge. | m = 3, ratr, 6o 3t = 27; 2) V1 =L rall,601>0i13=1i , rl-n = -s, raft, 60 (-3)3 = -27; q 4,Ei =2, rax,60 16 > 0 i 2a = 16; $ 4-16= 2, IIi,60(-16) < 0, a noDrHHo 6yr tria KopeIIeM lapHoro crereEs HeBia'€MHe wrcro; a {-n = z, :gi, 60 2' = s2. 299. 1) {6 = 2. rlrcro 2 e apn&MerlI.rHllM Ky6i.{Hr4M kopelreM i3 'rrcra 8, 60 23 = 8 i2-qnc,roEeBiA'€MHe. 302 llt AnTEEPA Mepsrqx A. r. ra iH. AKaAeMi.rHr,rn piBeHb ii::lliJ::.:.:.::::::i 2) {,6T = 3. .r{I'cno 3 e apr{bMernqEnM KopeseM 4-ro crenelrn s.rncna 81, 60 3 > 0 i3r=81. 3) 3 He € apnoMerr..rlrrM lropeHeM 4-ro creneEs 3.rl'c"ta 81, 60 -3 < 0. 4) qrcno 10 se € aprabMerrqHnM KopeHeM 5'ro crelreHs 3 ql{cna l0 000,60 105 = 100 000. 3) vo,0016 = o,4; ry fo,s66s1=-6,1; " f#-m=;='i, r frJ=-'. '; ",62s _ ./s' s ,2 . so1. n {Ear = "J?" =7: ,,i/trl-l l, 3 3 :t o,r.{:on=o,r.V z'.z' =o,E (-zJ z= 2l 4) -siF#=-8iF;= '( i)=,' q[n'={n=la"=s; 6) '"irAe- = rovtr). = 'oifi@ - ?. 3o2. 1) (J11) = 1li q,E)'=-z; ?r (-3vl0l = { 3f lo 8l I0 = 810: s, trr,[El".lrt".qe I €=9=g,"'l.z'=".1 -!2r '"- 64 8 4' o, L gt* =! n,=,n. 22 3OO. 1) J0,25 = 0,5; 7'4 110,125 = 4. 0,5 = 2t sl i6'=i6i=s; 303. 1) (i4B)" = 1s; sl (-{/ii)" = -rr; 5) f lad =i 45=15; zl tlzta = a; zr (Vs) =s: b) iF= -7; 3) (V?) =7t 6) l5V3/ = 125 3=3?5; 2r (-VsJ - er +rll.t,Eol=l45=9=11;3 ,r 27 3 3 6) ( 2V 5l r 2r' (J-5) = 32 { 5r 160. so4. 1) 0,3.$[boo-s V25o+o ( '{6)" = o, a . ro - r ' z r 6 6=3-1o+36=2e; 2) Jr4'-t-2Jr0J t t2a='4-t 2t' 10 2 t4-40-2=561 5/ i ? 5 Is t2 3 =:t - + + 4 2l A A a I iiiifiiilil:.i:ii AITEEPA Mep3neKA. r. ra iH. AKaaeMi{i{ri piBeHb ii'.1 3o3
  • sos. r) 200 i6,oor - 5-63oor, --alz)' zoo o,t-{-0,2r-16 2= =20+0,2-32= 11,81 1<o zr Veooo.l/zoE {ve)"'vrz -20.q r8) .rr.'oo 8 ,,r' ! 81 3 3 = s3l* 25 = 5s1. ztr.t1 {i=-21 .r=-8; 2) ili =-2; "ea; U {i=-2 t=-Bz; l,lix z=o; iTi =2; sx=ror r=s]; rl i6r-z=o 3x. 2=o;3x=z; r=?'3' q lb' 2=2i 3x-2=16iAr=1Atr=6. 312.lr r:3 A2f + 81= 0. Hexafi r.a = t, roAi t, - 82t + 8l= 0, t = 81 a6o t = 1. orxe, ri = 81, r = t3; ,a = 1, jr = 11. BiAnoqiAb: !3. !1. 2) tc6 +:.t - 56 =0. Hexeii jr3 = r, roAi t'+ t - 56 = 0, t = 8 a6o r= 7. Orri{e, x' 8, r 2; .r" 7, x !7. Bidnosidb: 2t PJ1 . 3) ,rr': + rd - 12=0. Hexa;16-t, roAi t2+t 12 =0,.=-4a6o t=3. O,rrie, r.d=-4,r€ O;t6=3, r = Xeh. BiAnosiAb: lar5. -25! 54=O,t= 2a6ot =27. - T=t--)/.+ , 306. 1) Vr+6, r+6>0,r> 6.fllcqo.r'€[ 6; U to tO. flKolo o = R, ro s,{par Mac aMicr. s flE@ -1r, atu - 1)>0. +-), Brrpa3 Mae sMicr. 2) ts = 12; t=!!ltt 3),r1o=1; r=11; 5, 15 = -32: t -- -2,, 6l!6=-64',xeAt ffiI'ldf:rg$ i:.1{.ii}:r0 ':.:':di.tt$ ::!::::n:.t$ :;.:riii:rq il rl I l I l I I ;l 2) 4 6) 2) 4 i$ffi i$jgiili ,finnro y € (--;01 u [1; +-), ro Brrpa3 Ma€ sMicr. t !li, y > 0,, < o. sRrrro , € ( -; ol, ro Bvpa3 Ma€ sMicr. ' 5) V r', x' > 0, x' < O,.r = 0. .flI(a{o r = 0, ro Brpa3 Mae BMicr. 'Plx' -zx - 8, .r, - 2x - 8 zo. , ---,,--- --,,--. flKqo r € (--; -41 u [2; +-), ro Bnpas Ma€ 3Micr. - a ; 3O7.D s=4x-2, x 2> o, r> 2,, e t2; +*rt 2) v=!4 t, re n; s) '{2' 4, 2x - f > 0, "(2 - ") > 0, -----Y-f=f- ' ' . t0; zt; o2 4) 9 = --_:]-, x, 4! +4>0,(t-2),>o,t*2,r€ (-*; -2)u(-2; +-). llx 4xt4 4)ta=i6ir.=!2i 5)16=5; r=1{,6; 6)xt= 81tx. At 7t27xt I Ot27x lt r' l, * l, 21' - 3' 8lt.r- 2)J= 125, x-2=5: x=7i 9) (' + 5)1= 10 000; (' + 5)1= 101; '+5=10a6o'+5=-10;'=5a6or=-15. 313,1, x6 25x3 54 = 0. Hexaii f = t, .ro(l t2 orxe, r, = -2,, = Pl-z = -Jz; xs = 27, x = 3. Biano'iab: -1,E. 3. 2) ,3 + lAx4 - 4a=0. Hexai ra = t, rori r, + 13, - 48 = 0, r.a=-16,re A:xa=3, t = ):1h- Bilnoai't t{3. s14. ,18 = a, sxqo a>0; z,[V = -a,sxqo a so. 31s. 1) J;t=bl; 2) -o,4.{V = 0,4c|; a) ,E =)""); +, J^" = ^t=^,. 316.D Jn"=n, sxr']o n >0; 4 E6p' = 4p, s&s{o p > o; 5) lf,f, = cu - c': atz. i) JoSl -:o = 0,8 6 = 4,8; ^. Et s 1100 10 t = -16 a6o t = 3. O?:*e, 1F= n, rrxt4o n <o; .,63e* - -o,or, s&rqo & < o; ,!,rr{t - o,stl= o,br?, a<o. J6'.s'=6 e=b4; ,lra Ezr rr -s ! 36 'l 36 6 6 309.1.) r'= 1; ,r = 1; 4)rt3=0;jr=0; /r 1 7t64x5 | 2 0i64r'- 2r'-il A''- ,, 8) (2.r - lf = 8: 2x+l=Ja:2x+1=2.2x=1t x=f;1 e)(ir- s)6= 72e; t-a=fV2e; '-a=Vtrr "-a=i/F; '-3=3; '=6,.r-s= -{F, r-3=-3,a:0. 31O. 1) Jr=9: x=81: 2t l/r=:: x=-:-:: 3) {/x=3: x=81: 5 125 4) {i= 6; x= 216; 5 li=-2; xe a; 6) {/t=0; r=0; T {2' +7 = O; {2t = 7i 2, = 44Ai r = 171,5; at l2t+7 =O;2t +7=ot2x= 7; x= 3,5: g lfLrj 7- - 7t 2r + 7 - 343 2r = 336t r = 168. 304 ll:i ATITEEPA Mep3rrK A. r. ra iH. AxaAeMirHur pieexs ii!:.!lfilii:* 3r8. 1) .v6t..8 = .r52, = .rGZ = s; zl ,6oo . Jo, re = Eoo . oJs = .,66 = o; q Jl:.Jt.1i26=,fu.2.%=,Ed = za: 4 E3 tE.s" =tE 4 =2a.32=16 s-r44: o f =n$=.ao='' -. vE fs fi rol -=-l-=,1 J48 ! 48 V16 4 ,Ez t27 /s.3 3 s .6 f5 /r r '' lt+z 'ltqz "lt zt .z.z 7' "'h.Jt2 -Va ts-Vs s' i:i!{il!:iiliJ:111 alresPA Mep3rsKA. r. ra it|. AKaaeMiqHlri piaerr li:i: gos
  • r 3. Bracr[Bocri xopeHr n-ro creneHt 319. 1) {6a.lx=+ s=zo. sl !21o.7" = t.7 = 4.7 = 2a; 320. 1) i/0,064€43 = o,4.7 = 2,s; ",8=+=i='i' s21. D 1!8. +E = 4!G =zl ,r ff=1ff=,.,0'=', sl 'E' . r . Vs' . 5' = 98" . 5' = B! . b = e . 5 = 45; ela a 6)1:::::: =:12," 73 =2".7 =8.7 =b6itl2" 7' zl .,[i-6. rfr..,,Ao = t,[ zr -ao - t6i = s; z) Vo,oezs. s1 =o,s.s=r,r; +; i,6" rd' = 3" .1s' = 276 996. z1 163osr. rr' = 6,3.11 = 3,3, o, uEl ll -r' ,' a s -72 2zz. I 5'' 5' 25 25 25 zt Vo, ora . +4 = i6-ozro = o, o; ^'i ="[t=,E t- V128 !r28 !32 2' ,zs. I Jni' 7n -7n. 60 n zol D {rzs'.- = rn"; ;lf i6,ooooor- W = lo,tmun' =o,+^"n",60m>o,n>o: a,l tl,,t"* =)*"""1= ^6n3, som>0,n>o. 2' kli =,4;. sl '{"W = Xlo'a- ; - .d-: -. -7r '1/8r '{3' VB: sr * = i/', '9,.' ,t, 'V*' t/ x u F,tr" rF?^ t,",, - r^^". :Jm"n' rm n na.4 .ld" ='G: q 4"" = E; ]zz. rl n[rE = E, .rr VF = {,6t; z) Vaa = iF = i4; s, 4n" = llo; er c[6 = {F = {,Ar e) x6.VI tEt.ict =.€. zz . i,6.1-ey = 3.1 3y=-e. ro, fi. f'o =,Fm - rriu . ".v35 ! 35 szz. tl fllzi . ;uE = Pls' = r: ,,8 ,l'o = rrG ",i/5 I5 g dr" .5" .4* ni = I.t7' 4 = 23 . s = 4oi +r $1- ro r[t'.-." to-, *t " : ro' . I o. r, Vto'.3, 1 I0".3" ' l0 sr i/i - "/i7 Vg Jrz = ilst tz =tlu st el l,E.,m tn nli"tw -ro - l6a - roo = tf az = -z; t, v-"Frr6i=ry =4,6+n ='4.8=tz: al J1%.Jis ,E .,.60 ={tr*8o..rEe'r=1181 . ,1 . ../86 = 5 . 2 . 6 = 60. 323. 1) tGr3)' = l-1sl= 13. z1 {-oy = s; gZq. tt .t6"" =lS" =5r,, 60 a>Ot 2 iEtn = st": q lEE"-t' =lr""al - ba'b, 60 a > o i b > o; q ltFzg""W = Ba"bs =Basb', 60 a > o, D > 0. 8) {,G6* 10. {,GG_ro = iG.gI - t* = vior -t* = Va = r. :r $[ e,' = -el= a. a '4"" = {i; or 987 = Vs" = "6; sze. guoo '6. ro6ro d - 0. t) {a'; 2) Vo'; gl 'Vo'; a) 'i/7; r) 'Vo'' e I '.Vf,;. 329. Vb, '106'10, € fi. D ilt'; z {d; s) 'V;;; 4) '{6'. :so.t) Vo'=o; d: o: zl {a' = -a. a <o: :t i,fT a; a - n; q 11"" = ", "=ot s1 lQ sS =11,E-r', o,-s; 6) V{o 5f =lva-5. dcR. :er. r1 $6 = o', o 2 6t 2l a"" =-a', a<O; 3t Va' = Val , a>o: q dd = {-;' , "<o. ssz. D l,l"t =+6.+lo, o>o,b>o; D <l"b=1 ".11 b. a<o,a<or 4 { ab=X6.Ilj, d>o,}<o; qiffi=rl;.X6. ae R,be R) 5 XGb = {-;. {j, a e R, b. R. i:l:lttllJllt:.lj1i UTeSPA Mep3rcKA. r. ra in. Axasemivnrii pieenr i{f D lxE =flr) o "{"-u = tEi; ", E=,F =a. 3OO lrl:ArrEEpA Mep3neKA. t-. ra iH. AxaaeMi,{Hr4t piBer" lfiilillli:l:::i;i
  • a> 2- PiBnicrr, BnKoEyerbcs, sErqo t € [3; 71. s) XG- 6X' - 10) = {,6-. {6 r0, : e R; 4) i/i;1x,+2X'+3) =tt,.U t('-a {"-a), - r > -1. PiBEsIrHs BljKoHy€r6cs, st(qo t € [ 1; +-). '{6*q' = lpuq'l= p'q', srrqop>o; 'tr;** =1n"nl= l-^").(-n") = n"o", .aftqo m < 0, n s 0; ab' 1t7*b"%4 = ab' .la"b'ct - ab2 . o1, bs . ec),, = ata"cn, s&!ro 6 > 0, c < 0; -qfr" . "E-" !: - -an'p" .'h"tlpot 8n'p" k'6 pto -o^,"1..k' 256n' k' 4m" 4 (-n,)k' -"P ^ ' m <O, h>O. 338. 1) i6t > l/Ft sxqo a > 0, 60 EepiEnicrs a ) lal rr.monyerrcs, Frciqo a > 0; 2) iF < Sf,'., flxqo a € E,60 HepiBgicrl o < lal sx!{ogy€r6cs, srtnroo€.a. sss. rt tf' a=lol-o. a a=2a. ertto a -o; zl la" +4V - al+a=-'a+a=o, m{qoa<0; U ,[a" + l/V =o+ al qr Jx lla =lol- o. sss.U lxz -n= dx-z <Jx+2, 334. 1) t6{ = lbl; o {68 = l"'l; 33s. 1) 1,2rV:0 = L2l*; q'{@-0- = a-v. PiBsictE BrxoHy€rr'ca, slirlo r € [2; +-). zl :F - s(z - xt = lE4 lA - r, [(r.-3)(?-x)>0, f3<xs?, lr 3:0. lr-r, 3<,rt?. lt-"o, l*=t, r-2>0, x+2>0, r' - 4>o; lx z>o, l"r+2:0, l[; = :;, .it 6) 7) 8) r ti::iiii'-{.}:.:.::j: ,lrSitfiiji!:tiixli :lt$ri;ir::il*i:J::i litl#-&i':fli 2 [l-a<*< z' l(x+1)(r+2Xx+3)>0, I ", -r, l-r+120' ll*r.0.lr+2>O- I I 1v+2>O- lx+3>oi l**rro, -1 <t -1 -2 z1 -0,+{V = -o,t "l: l,[iF = n": z {u- = a"; 3) 6) '3) t[a- = a"l= ""; '.3G-o" =1,-51. 9"' = la'l; 310. r) {, +a)n = r + a. Icnoci':lx+4=x+4i ), . -n. J' . -4. l-x 4=.r+4: L2.r=-si I,'- n. !,. n. []+4=r+4i l0,r=0; BiAnoqiAb: t4i +-r. I xe Al: 336. I t {/aru = rnl - rn. qxqo rn 2 oi zt !r^ = nl= -n. rxqo n < o: {t6p' = 2&t-- 2p, snqo p > oi q {zsen" =zpl=-zn, sKtr{o}<0; B ,@ =b'l= "', s&qo c € .R; o1 16-zra' = o,sla']= o,5r?, sriqo b < o; 11 tr6""5 = slt"yl= ax"y, axulo y 2 o; el .,6, o1o%F = o, r lo'bul = -.o,ta'ou , sriqoa<0,0>o; s) -1,2*,h4x' = -r,zr,.al,u =-g,or'( r')-9,6ru, s&qor<0; *,'la:.,,-:=*;' = 4*+, " . -f;.o,o.0.o. ssz.t 1,8 5o^ = rl"' =so'; z) i6, ooorf" = o,r a"l= o,1r', sxuro , > o; gl -r'[a'" = -s.zl" = r0 (-r) = 10r, '1Rqo , < 0; r; o,ri,fiooo ooo"" = -o,t tolz'l= -z', z>o; 3OB l:ij AnfEEpA Mep3neKA. f. ra iH. AxaAeMi'{Hr,ti piEeHb x>-4. tt ""o"ia: tr@++f = r+t, {,+qn =lx++=,+t, nnllle snu]o ir + 4 > 0, r > -4. zy X{r-r'y =6-a,f, {6 s,)'=(1-3'f =(1-a,),, qe Mo)rirnBo, gl{rqo r 6 E. rar.rl i/(G-z)"=J"6-rl - n/Jo -2. oo Jo '2, 2) i/(1 -,E)' = Jh - .,8 = J-r + Jz. oo ,E ' r, 3) 4') i/("8 "5I = q/.8 -,6r i/rJe z)' = Vl"6 - ,l t/ J5 * z. oo Js . s. s+2. r I fl(,6 - z)' JJs - zl = JG 2. 60 ..6 > 2l f- -- zr V(G -.,4)' = {'va ,al = 1tfu = -i6=. oo ,,5. Js: ar ((Jrr-a)" =dlJrr a = {Jrt -s. 6o JiJ,B; t;"r- 4) '{{J? - 3J = VJ? - s. :iill:iiliil:iit: AITEEPA Mep3nrKA. r. ra iH. A(aAeMiyHrn piBeHb fl.! 3O9
  • 6)tc<o,a=2r x=r; 3a3.D s=a,,8 -x= xl-r= = x- t= 2t, fiRqo t < 0; z1 s=2r+[ru =2x+ xl; a)r>O,U=gtt et u=fr.2=fi,2. s=4+z=i+2, t> ',=!a2= f +2, x 3aa. D !={V - 2x =lx -2x. 2ra=d=.d-r"-dj= x. g&qor>0, toy=r 2x= x; s&qor< 0, aoi=-x 2t=-3t' flriE{ot<0,ro6roy=-1. - t/,"h6) U=-=-. xx OA3: r + 0. .fKrr{on>0,roy=1; sKrqo t < 0, ro J, = -1. 3a5.*lV=r-a. lr-4>0. lr>a- [l:r =x-+: lx=x +; reA. ,, 9F OA3: .t * 0. 0, <0; t>4, O-t= 4i 2r'{f =6 h lo-r>0. lr<0.I rno.i6: I I lxl=e-x; lr=0- f1* s o. [1' s o. ll-'=o-": llo,=e,.t 10..r s 6. lJ0 < r s 6, !'=o-,, [1"=:, II cnoci6: zr y = iF. J"' vl' .JI r = J, , l'r ''.,>0. 3 I o :::::: AtIf EEPA Mep3rcK A. r. ra iH. AKaAeMiqHr4f piBeHb l::::ii:+:::i:::::::::l lr+3>o- 3) 2Vx" =r+3r l l2xl=r+3i l-= L l'=: BiAnMiAb: -lt 3. F. ". l2lx =x+3; J-3sr.so, l-2x=t+3; I',0, [2r=n+3: I-3 s,r s o, l>o, q y={1' zf =,-z; t) v=Ji {'" =d"' =', r.>o; sr u = .y',' V*' = lr.l'? xL' = lx ; BtAro6;ab: pos!'s3RiB HeMa€.
  • 3a6. 1y !F=x+a; 3s2. 1) .,6 - ./1t1../6 = 1.'6 - z.'6l G = -,81. ,6 = s, zr iz-,6.1'6+r =(z-€).(,6*il=z.f +z-a-"6= 16-r at lb - ,t;1. lb l;l=lJbf iJ")'l= a - "r; ay lz s."i5l' = (-z * su6)' = a - z. z. aJ5 * (a,6)' = a nJE + 27 = st - tzJs. sss.rr *= L2f,6- =rJ6, J6 J6 J6 - 24 zals a"6zt-=-=- 5J3 5 J3. J3 5 ^. lz JrkE-r) $Ur-n - E;=@;t(!trt= ,-1 erz. {"-#'iF-'f =2t x-sl+ 5 xl=2. Bacrocy€Mo Meroa i'r"n"-i", r ftQfi ir<,q lr< j. [*.3,r=s; tt1,,*t-u-' 2: {-zx- e: l*=a' - ", J3.xs5,'' lx-3+5-x=2: 3){'[r-3 5+x=2: BiAnoaiAb:l,el3i5. ale. y = 1,@ + rf *1[:-F = lr + 1 + lr - sl. SsaiAeMo nyni riAMoAytr,Er'tx BLpaBiB: r - 1=0,.r= -1 i jr 3 = 0,.r= 3. fitrqo r ! 1,roy=-, 1-x+3=-2r+2. OT)+ie. ^' 2x + 2, t s l. fl&nlo -1 < t < 3, ro t = t + 1 + (-r) + 3 = 4. Orxe, Y, = 4, -1 <t<3. gr{qo t > 3,'roU=x +l + x-3=2t; 2. OTir|e, As= 2E - 2' t > 3. ll-ss,cso' f1-s<'-' o. l"r+8>0. l.r> e, )r-.r-ar llr=-a; llx '-a: lr '-a:11"0. J,,0. l)x=x+a: Io.t-8; l-.1, Lr=21 BiAnosiAb: -4. f6'-10>0. 2t Vr" = 6ir - r0: l lJrl= 6.t 10; BiAnosiAb:2. 34e. 1) 3145 = 3 316 = 2"6; ar S"Eoo=fr ro"E=.E' 350. r) aJ13 = ."6.rs = d1?; a) e .,6 = ."66d; -5 r=6r-10; !r $.i!:;i::::.{.::::$ 1l$z:r.tl$ jiii,ti,yr,Lidri:il ,:q "!.11:.:.:..1:.1:.: '' - 1 :!:i.:+:.r.t ^___!_rr,_5r-(/,.##;='u(fl;f )=,rv,,,r,,r, CilNE:'=- :=-:icq{2 (Jrs - J12)(Jr5 = Ji *16 rs(,,!B*"/iZ) Ji t "ti I3"t5's.*<s, 10.r=0r l"r5, ),r,, ".a.l2ir = 10: I.t = 5; 1 Ja Jb ltE - ,tE)(J; - .tE) a - b foryeMoca rlo BxsqeHHi HoaoiteM]l zt )Jna=)alz=+Jz: 4J -o,o5G4oo = -o,oo ro.zJrr -Jrr. zl -roJil = -'4a. ioo = -Jlaoo; Ij 4t -;J54 = l; 54 = J24. I I ,, -,ELL= Ji r,li _ (J;)'*(.6I gsr. r) uqb - oJ5 = s'6 - 4"6 = -."6; zl r,/iz - z.',6 = ro"6 - z.'6 = 4"6; el ali,-tuT+zude=s 6E - a"E +2 7E = BlE - a'J,+tttE = zsJt; 4) 8.,6 + .,[ 2s - + t62 = a. zJz + e.,E - f, . s,!z = e'E + a',8 - sJ, = tt"E. sss.ry u@I.ffi*a =.[7-ro =r; a (ffiG $ - 2.,6)' = o * zG - 2,,(o * z^,6)(6 - 2;4 * 6 ru5 - = 12 - 2.,Q6jl =12 z. Jte =n-a= t iifli$illjtif AITEEPA MepsrsK A. r. ra iH. AKaaeMiqHnt piBeHb }i:!: st3 ".o.'r fr=@jp=6.,, ^. a- b lJi - Ji)(J' , "rt) 'la + ,lb Ja + Jb ^. "E-t Jz-t r JI J6 J3 J5(v6-t Js 3' .. Ji5 '6 v6(G-€) J5 vit ' b J1o G(,6-Jz) ,6 5' -. ra ,45 ,/iT(,/i5-r)o, -= +=vlit-t: v13 ./13 ^. "*2"!oa +a Ui * Ji"o, -=-+.=!a+JD: ,la +,lb Vd + Jb I = J7 -l;;tF' -. aa+ali aG*'6) 4 " -;r - 5 = G - JF)Ta + G)- = ;Gr "li * '6("!;.Ja(,E ,t.o - ^tr) 312 li{: AIrEEPA MepsIqKA. f. ra iB. AKaaeMieHxf piEeHb
  • ss6. 1) !,:-" =C;; =l^^lJn=^'Jn; 2 Eo" = oJi+u = o" ualu$ = a't6 ,rG = a"b6.tE, a+0; a, Jim z,"lJy -zx"Js. x o. q uG'V =sl'1v'1J5" = -slx v'nE; = sxs1.t6;' r> o, a < o' 357. t mJi -.hn', n>oi al prT = uF, p>o; 2) sn.,$ = JsVi = n[in", n<o; 4) lalxn=W, t>o, a >o. 4. ToroxHi neperBopeHHq Bllpa3iB, tKi Micrqrb KopeFi n-ro creneHt 3se-1 1.t86 = ilt- = 2El zl +En = a,Ezs z =t<,E; U tEu - +lza = s+tz; o fzzgo l/i' ro :''fl.o, s; <Er],a" = l[e.6 n" -" = z":tli"" : a1 t[ t =11 "-" = o"11;' 7:) d-b4aw = lt n . rd av = -zot"ttz""-; s { !o8a,b- - t[-n. 4d'. a. b" . b = -s,a"o'{aab. sss.,,-tvto = f,slz= z"Jz, a *1640=;ic€2 5 =itT-=!r$=;lE, a, f sae |t[i ] rtz xE +1 -r,z16e = 1,2{2" 3=-t2 21JE = -2,4b. 360. 1) 160 = i[6 '5 - 216; zl *,&s6 =l/t 2€=sV6-; u Jin = "ul7 t" z = s'Jz, at 16o ooo ooo = tot6; b W =1P zo" ; =s u"W' et {6Jsa""' IE Bb' b ,'" " 3 b,'ltE; sor. r) 2.,6 = 1Al =.,/ir; zt t{8={q"i=6at=I'b2f; 3) r0f0.27r -fio'o:zr= rDzro, o,!ut, iffii /*, o ulloa' = lEzs ont, =:,!ii; 6, 2{6v = ilniv = illeul 7tblab dt-w .Ja,,", t,"{i-{X Vfo :or.rr ]*ro=]r,6" r =!.au"ls={s; 2l 3) 4) 2lV=Et=./16.7=^EA; rdG - +Ezr. +" = +E:r,o": o,BltrooV = lEsn .too"* =18i7; 363. 1) ai6 + 3i[ stG = z<[i; 4 6!b + 2a,6 - 8!b = o. :y r{,6+aV--{,f, +rplV =sr!; *e&E; 4) s&6 216 + 8V5 :i6 = oi,6+ 0i,6. so+. rt s.t6--z{6={f,t 2J li +7!b -ar,tE = aE,. 36s.r) t/625 V320 -vi35 r1+o=i6' s 12".s-i6'.s 92".5, =stJi z'tuB -ztrE + ztE=ri,6-al6 16=o, zl {san + :!-td ; {-an - t,slian + +lq+s* = = ztFi - strFi + a1,E; - 1, E. 2{ sn + aFi = B1fti + o = s4lii. soo.r) VEa si46+svi28+{t000 - BrrE s.24r+s.4(t= = BltE 6{, + 201,8 = 27tr8t zl i6fii +eXE6a z+,EG + t4tzgu = s{i * a<,li - e+ri a<[i+t z.ziE= = 111,G - 6{; + 24!!E = 2sd; . saz..lzJs = t[q.B = xE ; 2) V3V2 = {Vsa = Vbai s, 1{;$ = ,{{F =F = ti, a > o; at tEtE = tl:[t ="4u, t>o; sr i,fula = .il14G ='i;t = .77, 6r y2vrv2 - VTE W,rze = vrze. soe. rr lojo vi," - il," , ' o, zt ula,f,a = kn = ,ln, s) i,6.,6 = {,F ='3F, b > o; 4) W" = xF6 = flW =.Vc = {6, . > o; sr V''V,' = Jq/r' .e/, " = V",c', r'o; u, fi-,/"v, r/F=v"c. (/,c-vf, {a.={a. a .o 1 I l l I I I ll I l I .^. -- -li i::i::i.fl ii:::::IJl iii:::ii{N i::ii:ii*l l 314 iii: AIrEEPA Mep3neK A. f. ra iH. AKa.qeMi'{Hnn pigesu ::*:ili:!i:iJl:il:j i:ii:iiitiit{il: AI|EEPA Mep3rrK A. r. ra iH. AKaaeMiqHrt piBeHb ril:l: 315
  • sos. ry (r + Va + {fr)h - la)= r - ", zr (r *,6Xr. l6Xr - "6) = (r * G)(r - €) = r -.. az o. t (G *'[i) (di. {t)(et . et)(.v6i - pl;) = (G . J;)(<,r; . i6)(i; - {t) = =(G + J;)(G -J;)= n-n; zt (l; - tri - !o){; . '.ta) = J; - li. gzr. n .fo l; = "17 "l'" ifr, a > o, 2 J; t6=flF :lt = {f'0. o>o,b>o; B) {1; '.i6 ='d'"...v''' ="!^oo", n>0,^>o; o, ,!4 =,{"_ =,4V = r1;. o , o. Vo 'Xa" c'E t!!A p!;a /o d .. vz,r !z !r ,,lz t vlnr . td;-r, -y'0- - -de, - rJz. e, - or V"/" V" = Vi6; 16 = 'ff V" +17 ,lo - dJ; o z o: "'@ '@ f,-=vlg=d*=ra, .'19'v9'v3.'v3. et lm p,Et" '{"* ='{."b" 'fao' 'W =,{'w =XFt, =:["'a"l n, t/o'a'Voa' - Vl_d %''"_' ,t1 =,F. a > o. b . o. Job {a"a" 'lano' ! b 'l b s72.1 {; lE='{'".'{7 ='17, ,>o; ,t ,ly' . do' ='dr" fr ='il6 = ttr, st . "G.1t;=llF.{x.{i={"", ">o; n, E=E='$."'0, _ ,E v5 qF iF ^Ei .EbrEF=rF'F=vtr=ls' at t["+ '{"+ '{'t" ='{"'a" '{A qW =4"w 4}b" 4"'b" = "fl|5t" =l7o", r>0, a>0. azs. r; (r14 + o,rq/ios - {.600)*E = r+6+ o, siEG - i[ooo = s. z* 0, s.6 - r0 = =10+3-10=3; 6;-; 2) Vo.2s{V4 + 3V32 - 2(/108) = Vt - 3i/0,25 3, - 2ir-? - 1 t 3 2 2 3 = ti 3) (2{E 2{6 + {/ioo)(Vio * Va-) = ro n e = r+ (2.'6 = .,,6. s = Vao); -f;37a. t t Ia{? 2 - r"Js, 51i, ; ). tB r.'6 + s _ a"6. L s/f . a = -4 3 2-9.3+5.2= 24=9+10=t5+10=25; D ""Jr-EtPp =s _ vzz r Vi2s = s _ g.s " z, ^. tV24 - V6l 4,,ia - 3J6 4G:3E- Ju -z ttz+a * Ja zJa + Ja - E"E aJ6 - 4,6 r ll :;,! ::::::l::::::: Iil! :i : ::::::l::!t:-{ iili::4:.:l:*lil: : r 4 :;r:.i!t:.!: 16 - olEz + zi/rrzs 16 - 6.2{6 + 2.516 .rs.r, l=t@ Var.,6".s_rVe _!r'Vs 16 Vs' e 3" -s'-t' ,, | =46 _ J=ra _E t _ z"lz_. tlz. V4 V64 4 4 4 z' +t ., ^LL = Jl!!- . r2f!l = -4i6r; V(-3) VB t/3. -3 o *=S=l!@=ura,{/8 V16 2 6) +=l!S- j -ftiT -g t {F -tr^.'V8 V8 8' a 4 ,'etr n'<,ln" ', r/n.=FF =-;=n"<|n". ".o, 'r ffi=#=',f =,ina, n, I _r"iG_ (G. v*' roy -ii-9-, r':-!Et::!j =tEt.V(d+tf a+o szo. r, f2 =1$ =nvs, ,t #.roJr:.l' =:tzs, -! ,<li=otts u ft=f =z<8, n, -rs _ rsVzz' _ sVa" b.s'V3 _../". ll27 27 I ., lo {hooo ,--^ - 24 z+{te, s.z"dz ', vro- - -v-i o = vroo: 6) i; = ::r-;" = T = rroE, ,,1. *E ttu, " t;" xf' =m.d;. n .o. i:l:::l::ltiiltl AITEEPA Mep3rcKA, r. ra ifl. aKaneMieHhi piaexr !:iil grZ -----------il4 -1-12+10= 1; 316 fil: AIITEEPA Mep3nqK A. r. ra iH. AKaAeMi,{Hnl pieenu li{:iiii{:i:i{ri{:i
  • szz.ttN!-j=t@Lr,_JJ -{{6-vbrlq vb) ..i1, '6.a 0.4 o, ", tE l^ {. :l; :r ,n>o.n>o.m.ni '' L^-Jn tv,'l -'6)(v,zr-v,) Vln rV' ,, .,/i - q l'/,- rlln' 3) v, r. ,, , o, 'Jx+3 'Vr+3 ^.G,li r,6,t/'" r) 6'' .^.o,-' ^ l^" lF(.f'" r) ','(.fi t) ,. ,t*, ."1"_! d"tlf, -,[x q,a{i6 -v,) -"J;r, " o, b oi a - h, "' rr,F t;6 ,totfa ^. tE ,'{oa 'tlub + tb o>0,b>0; szg. rr =r = (vt)' " vt * r V2+1 ("8).*r, ^. 2 z (lDE * Jis * "61 "-2r *',. - '-"; ";" '-'= {zs {4s "6: 3, 15 rs(,6-r)_.,"6_,,. - V:o r{/o t o t + ----!- t(f '.{o) l,16*oa),!2s-t2o+t16 s+4 9'' =!+-l,Ett.3' 116($* $) '{6('it -'.i6) tr Gll; -'l;) tt; .6= ra6-6=O=v;' 9) ("6 !(i6.! "t(G 1) m'O,n>O,mxni (V, Vo)(@1. jg!:141 ={n *l,toa*tr|t", o't, tE t'b o, olo ali -.t*(J," -Jt) - Jo -Ja. , o.a u, Joa ..lab rlii + tli r6(i6.1) 1 5r -i :: :- --b' Lo'Oib/oi tla"t:' + va,t Va'b(1+ Vbl ndD 6) sLr,3 vgql--! i/27,r. v3 i3 318 ltt AITEEPA Mep3rer< a. r. ra iH' AKaaeMi'{Hrr pieeHt il::li!li:!!:::iid A, b _ s slJro -1./r -r) Vra V[*t V4{Vt6 v4,1r 2 "J2 {tla - t) :lz1t . t1 Jz 2 3so. 1r =1 == (if' q[t * i,6t). la+lb d+b zlvs vz) . "," ,,,.- {sr v63 rv49- g 7 Bt -"=.27.. . "11'0. 'l Trf.-'r,Vtoo-Jrorr lo I 11 n, ),-- rl(g. aVr * vE5l =.lg3d5'V25) o,r(s ra{6-uus). 3 - V5 (3 - V5l(9 3V5 r (/25) tr 3ai. 1) i/a'D: = abi6E, a >o, b >D: zt +lo't = ollt, a > o, 6 > o; tl +lo^o = o16, d<0,b>0; 3 .D +[-n" = [-n n" = nld;=n"d;, n<o' 2t il;trn -la,l. * 4,li = "'lb" tlb = ,Lb"{b. a > o, b >o; 3) ![11 = ,t blflE =, sflE,x+o; q lEz^'w = t,!i . z*'" . *, . "'" . " = z. n ",ltli^% = z^' "' W;, sl tlten'tw = z ")lt"lb"l,ti = a"""t"J2=-atd,tE,c<o,a>o; 6) lJtrW = {a," a'. b"- b" =l,,llr.lt[%,=lb,{6%.; a >0, D> 0i 7r 4i*u* =11;".*u. u" - a" b"l{ ab" = a"b"d_ah,, a <o. sss-D $za" =d22-'."' =z"du" = zalfia', a<o; zl d-ezs"' - d-s^ . "' - = s " {i - ra4[i, o.o. st PIdf =lat{"t="apJ"t, a<o,b<o; q :["^t* = "" r,'" :lo+ = o"lr'"1:["+ = asbsP{a'zb, a > 0, b > o. 3a4-D a!!E = 4f2a', a>0, t-",h zt,nl i, t"",,.', {aa".a,o.b.0; a"b' o"h' :i{itiiliiilti: AITEEPA Mep3nrK A. f. ra iH. AKaaeMi.rHrt piBeflb .t:a:ii 319 ,,,,f ,t"Hr" -rt'uy'-*t) .r/o-ra. o o.a o, Vr, - avr 16 _ Jrl,f 11. ,4.a - (V, a)11tr ,,rV-. re) G - lt (la - va)(r,6 - Vaa + Vo) Ji {'t * {t 1,la - "Jat + {a ,n, z jE_ lE(.4 r) =x? r, rJ2 :12 -. Vr8 - "Js /a(verr) ./r. "'EIE={,8(v6.1) -Vt' 12) 'l'" -rt' ',8 r ,,G (1, - r ) ' (", - r) J;("6 1) a>O, 1 .-, "^. Vr -a =96+{a, ":'o,a:'o; Va+1 tf+t :li +t 1 3za. 1) ':-: ' Vo I (R/a r)(V, rl vo I J;, x6; 6J"- a-b 4;-fi=
  • I 1 lntn' 3t nnl *=l- *=lmnl be6 = 96b", D > o, a6o -iGf , D < o; a!-a=-ll-a?,a<O: at6t, = _l}t,. "t' = dVt", t < 0. 38s. r) c&6 = -t6c', c <o: 2 a{i =d7' a>o; s abd6 = !t6a'b', a<o,b>oi qt awl l= = piei ". =. Vro,a,. , o, ld'0" a D' g a1[4 =-d4, a<o- ,,[Y f v, {6JIrf.,t v,, . l,'-xF 1" rb)({x - tln -t[t') lo -+EEtt[x Ja 'lb (Vo - Va)(V, + Va) t" 'tlt " +F t'h '6r (v" - "6)+G -to)- va tlb ----- iJ; atlb - +lV y*Ei *Jt" -<,F,tl"t +tr"t -+6 -Ei 4) 5) 6) <li * <lt" . :,1"t kE * "lta, -:= Va; (Vo + VDI V, llt" , {t" **[a" *El7 24bc -2{V Va+t[ (.,tr - JiJktr. "6) ktr E)(xF ttF) 4ao 6;4;= 386. 1) i6-t.&[el;6 = !fuIo 3' ft;ffi = = frt.-tr.E flilF = {,Gs .ii')o-l;J" = v1?:6110 = = i6or - geo = r; zt {i+-a.ls 'E"b.,={;;-"T' FEd =*Et-aTs a6;8E,+= ={u iTs.$srBG = 184" .8" i= {i76-s:o = dzra = +lte" = "ha =s; B) ffi-n'61-8G='@-T'tm-;m= ='{Tb. rfiE.'{61 - &tr ='61. 8'4l''i6-ffi ='vtrj- {5 = - ,So-r.ooo r: q .F+iTz. Ja -{z = {dAf . 5 ;a= ffi;ll."tl tc-E = = $* ta{z . +,E - t{z = <FF= n6 Jt - ETz = 4c6 rilzr 4 = 1ll. 4 = =,tr =2. sez. D F -iFz - <,E* "E = {F -lG iG;tr3I = {i -iTs 1,E;i; aG = =i,FjF('*G) ={as-a8=ti zt Jua-i tEs.qJ6 = t/(z,G t)' {zs+aJo ={24+r-4Jb i/25 ' 4J6 - {t:AE:tl1"6r!t r) (v'-r)' j,G {"J'=-1) -#.' lG-1 q/r -r (Vx-tl(V.r+t)(Vx t) 32o '.tlil AITEEPA Mep3ntx A. r' ra iH. AKaaeMiqHri piBetb llf;:i-:I':li!:!::1 <li * {t ^ 6 -'"G*tE.'. Vt+r=15-l .. "G+zz ( +G-z Voa gl - - t/a:' {;-"tE l"G.ze,G s Jarzz)- , Va r ",Go -s (V, -a)(,6-r) V,a s 'v" aV" -s-(16 -r(J, -3V,,el = t#-t(V;-3q/-r) = . (tG - s voa s) _ Vo - qf,t "v" (vo Vat. (fi ' a)(V' - sv" , s) G'zz ,E zt " ,G - zt v" (v, ,.6) ,,_. "'""; 6 --G-n -'" ,, | " G ^ -@- - -l -'.- z"u " l, t to - ?,t; ) = ",tb - "J". I Va' + zVac * V.' Va' - V.' ) l. BH'(oHycMo roroxHi neperBopcsFr srpa3iB: Vb"(rt. i6) '"6" _ . ({,6 . {6f <li ' <li' b-" (i/t .l;)(tF.+Wt,lV) "lt" **E;*J"" 'F J"' (Vb v")R/b if,l vilil 2. B!&osy€Mo Airo y Ayr{(ax: {b" do" t t|i *:lV -"- 16 * if tlt *<li itr lF (i6-*6XVa+V.) "n.-ValF=- va v" rvD-ic: ^ {tr {,t (,.6-.[)(,6.r./i) .. ' "{fr.*[ ""-;; ';"'-]!=l/b-{': a-b 11 rl6) -----------F- :l , - ',lio, tla'-!a't tl"t' t1a' 111' ,0, ('a .6XG -.6) . li *:li xtr (<l; - lb). l,F (d"' @)' 4;4i ;{iili.li'iltli AITEEPA Mep3rcKA. r. ra iH. AxaAeMiqHrr piBeBb fl:l 321
  • --- I I Rr r) V. Ji.t.389. 1r ii --F- , - tVr t Vr , Vr 2v' I =# q-E -1trr,(V;-r,6)= Va-Va r:t" :la' tvo i6l{V: f) = ,, - Vr. {i6 - {6XeG - c,6) t/d - t/b lluu*o, Vo +S = 96+Va. toro:rcsicru opanr.'m'a' .l_.Err (,ar'I = (l/;- Jtt)(.v!:4 G.t '(,t*r)"F {" ' )t *u"*o, 6*1 = J' *1. Toro*{nicrr, rparrnL'a. tx ^ | va - ga r (Va '6')l . tE ua -'1tt'lffi ,li:Jt' df,'la 'vo--d,^ G u,' r (.,/a V,l ('16 i,)' 'lo '6 . ' J"-Ju r6ira -ilG)(t;y; {;.,bi' - +G !t, "ld -;,tb li la - Jo ' 1,6b - ""6k1" 'rE) . ' rlJ,,[" ,!ot-- trn -yrr -* -iv"-!bl" ".'c' va{Jo 16l V,(l6,la) "l'b l!'b ' iy"'vor' ,,a -l;:T (v,-vb)v" 't-' vb To.o)r{urcl6 npaBun6Ha. gso. rr i,[l;E + iE] 5.8 . :r,u*uii * ,5^f2 t lli - 5{2 = ,. r*' (i,[*rO-if GE)'=", ,. r,E 'r.'E,rJrl {t ,'Et , ti/G. *rrtt turt z tJz ,". r+or 1-ry (1fi * s./z - iit - 5it)= '", t4 3,=f,f+* t4=o,t2 2"+2f 4x+7' l4=o'a'z(x-2)+2x(x 2+7oc 2=0' (r 2(r'z + 2r + 7) = O, t = 2 a6o * + %c + 7 = O. PiBEsIlIrs r'+ 2t+ ? = 0 He Ms€ xopeHis, 60 2=1-?= 6<0' o,*", iF ti"E n fi - sJi = 2. r{uc,T o 2 paqioHa-'rr,He 'lr-rc'!o' a '6.,E - ro i,6.'fa ro. n",.* 16'6* 10 i/aG- = '. t- 0'6-ro-rii(o,r, ro)'{o,a ro) -si/(a,l 'rol(e,a ro)'-(e,[l- lo) ,,. zo - : . z1G.fe * ro * a . ,i6.fa * 10 - "', zo o(.utoGrro-ffi ro)=,., )c' + 6t - 20 = O, x' - 2r, + 2t 4a + lfut - 20 = O, x,('c 2) + 2x(f, - 2) + 10(' 2) = 0, (t 2)G'+ 2r + 10) = 0, x 2=O, x=2 a6o rc, + 2, + l0 = 0. PiBHsllHs rz + 2r. + 10 = 0 He Ma€ I{opeHiB, oo 4=r tO=-g<0. 4 o'*", .,6'6 - ro = 'Gfu = 2. qrc o 2 - paqioHanLse q'cro. 391.,iloepcr u, *o i,)O-ra,Z'v'ZO r+.2 q. ,qoBeaeHHs. ne""t i6o * r.r"E r So - l+'E = x. rliaE€ceMo ao Hy6a o6nasi qac- ({n *r4Jt. {n 14rE)" =,"' 20 + r4,8 + 20 ra.E * si,(zo n ra.fz)(zo rrf,z) ({60;lt$. ijEo tE) =',, 40 + 3V400 3s2.x=f.,40+ 6x=J.3, jr3 6' 40=0, ,3 4r' + 4a' 16r+ 10r-40=0, |@ 4+4:t(t-1) +10(x 4)=0, @ 4)(r'+ 4r+ 10) = 0, r-4=0, x=4a6ox2+4x+ 10 = 0. IIe piBEEEHT He Ma€ riopeull, oo 4 = a ro = o. o. 4 o,*.. 1E ttA po . u,E = 4. roro,$nic16 roBe FHo. ([pr poBs'sByBaEHi BaBAaHb N 390 i N& 391 Mor{Ha Br.iKopscroByBaru OopMynrj (a + b)3 = a' + 1a'b + ab' + b3 a6o (a + bx = a3 + 3aD(o + 6) + b3.) _ fory€Moca Ao Bl,tBqeHHr HoaoiTeMlt s92. y=Jt. r; y=]o,re =o,a; a = uE,u =t,z; y=uEooo =oo; z1 o,z=.,E, '=o,o+ 5.=l;, r = 25; 12o = .,E, jl' = 14 400; -q= G, xe s. 393. y=G. L A(16: 4), ./te = a, ran. fpsoiK OyErcqii npoxoAurr, repee rovny ,4. 2) B(49; -'lr, "6= z, "i.IpaOiK OyHKqiI He npoxoairB qepe3 ro.Jl{v B. 3) C(S,6i 0,6), .v6,0 = O, o, si. IpaOiIl OyHxrrii He rpoloanrB qepe3 ro.rRy C. 4) D( 36t 6), .faO = e, "i. rpaoik Syn&qii He npoxoaurb .repe3 roqXy D. "no. r' .E' E !3 '{5 4 "ls, , 'm; s).,65.6=.,66; q s"E = "Ei , "85; st ,Eo , zJi = Jn; .,.,8=,F,i.r =ff=a. = lu6 +]= "6*+; J{J2-r)'=l/6 il r5 al .,6*a-.8-e 12. 395. 1) 2) g22 ',t4: NlfEEPAMep3nqK a. r. ra iH. AKaaeMi'rHr4i piBett iiiili:ilitl'iii'i1 i:i::ir:iii:::irl::i: AITEEPA Mep3ncKA. r. ra iH. AKaaeMi.{H,fi piaens !:!lt 323
  • 396. 1) qE=-:c-1; Y'=./1; A2= -x 1' 2) v, = ',li; v"= 2 x.. 4O2- a=illl+2, E(v=[2; +*)) 4 v=di--+, Ets) =t-4: +-rt 3 v ={; -2, -a(y) = ( *; +*). 4o3. 1),finqo 1< r <216, ro 1< Vr < 6; 2l-72s<'<8, s<{; <2. 4o4. 1)O<r<256, O< i6s4; aos. 1) i,/i- > i,/i;; D 'tl-n > rJ z6; 3 2 " tlU-; 4) l,6..@t. 6. {6 = f,tbl s)'so.xa='vo+; el z{i = {u . slz = Jsa; 2) 16 <.' < 10 000, 2<i,t<10. li$ffi Bi]no6i0b:1.EtAno8tAb. poaB's3KiB lreMa€. zl ,E=!; v, = 'l;t 1 A,=; BiAnoBiAb: t. q v =rF t"+5, '': 4r. + 3 > 0, D(y) = (--; 1l u [3; +*). 4o1.1) y=(/'+L E(y)= [1; +-); 4 a = ,G 2, E(a = e*i zli $ v=li-s, n@1=P. 5. OYxxqir Y =f 397,y = lx.fpaoik Ol,EI{aii ryo,(oalIrL 'rep$ ro'rRu: B(1g; 2)i E(81; 3)jC'{10 000; 10) l I 39S. y lG. fpa$rts avuk(ii npoxoaxl6 'reoeJ roekt{: A( s; 4; B(*;;); r( looo;-10). 399. t) y l,G. t. aryr R: g = alx +1,, + 1 >O, t> -1, r(Y) =t 1; +-)i r:-, Srq-:i'-1. x -2'O.x/-2'Dtut t -: 2r-'{ 2: r-)' t}rr - ---,--- --7- a1 y=18 "-2,""-t 2>o, - Y Y ' r € (--; -11 !, [2; +-), D(y) = ( -; -11u [2; +-) -1 4oo.1) s = l;+ 2, D(i = Rl D g=E'x,2-t>O,t<2,D( =( -;2lt l^ sr y=r/'-^.,r -3, O.x'3- Dlat=t -:3t 13: -): t6 j,'o b ;(i ?r 4i/; {' " = ilaq z :lzsz . rV; = {" "' ffi, ', ,/i il? = {za +13 -/1:r3 vs a - +Er. 406. 1) .',6 =&/i% > 960; D XE = tr = ',X16 . "XEGI 3r srfa = !27 a Vros . a'E - tT z tT,"l q E!0,2 = {62s4,2=$zs >ro{o,orz =fo ooo.oprz ={rzo. 4o7.D1<J3<21 4) 4<V100<5; 408. 1) 2<v18<S; 47<4s<2i 5) -2 < v30 < -1; 2) s<{/isg<4; 3) 2<1/21 <3; 6) 5<-ve1 < 4. 3) -6 < -V212 < -5. 4o9. 1) 4 i ii{;0. qi,li qrcna, p$rarroBaHi Mi}li HuMI,: 5j 2) iFSs i {640. Ilird q'cna, posrarxoBarii Mi,x Hr.rMt,^t 2; It Ot li 2; Bt 4i b, alo.Ilini qrcna, posrauroBaHi Mi}Ii'rrcraM[ ,/iS00 i iAo' 6t Et -4; 2t r;0i 1;2;3. a11.1) {6=i66>G=V2?; 2) V12 ='.V144 > 96 ='{A%; 3) V3 =,V2? . V2Jz = VJ28 = 92sl q tl'ln =:,tii , ttr = "E = tE; 5) i6=16.ffi={Es; 6' irmt 'VBz ='dz' - tz 'Ja slz = ,[2. i;r::::iiiitiliii: AIrEEPA Mep3reK A. f. ra iH. AKaAeMiqHni piaeru lilr gZS 324 ri::!: MTEEPA Mep3rqK A. r. ra iH. AKaaeMi'{Hnr piaenu lilllliiliil:ii;i
  • 412. 1) G i 110; rE = i[ % < 1[40 = f o ooo, J-r.Vto; zt r1ta = "E; i6 ='gEs ' "t ='96t, r,/ie. V"E ' 3y 98. i/2",2 - J,s '{8. '{z - ffi, +> .liE = e,E ="PIn, {G = "!" = E',f iG. q1s- "Ji; 'tE; th zl i6; 'So; iE; g) i.F; {,E; .6r al i,[E' '.i[x' i,6. cr+. r) .,6; i4; i6; z) i6; i[o; 415-1 a = -lla; 960. 2t u=4x 2; {$ffi 326 iiti A'TEEPA Mep3reK A. r' ra iH. AKaAeMi'{Hnr pieenr :iii,:}illili:lil fory€Mocr Ao Bl,tBqeHHf, HoBolreMr,t 417. 1 = 2o., 2 = 21 ; 4 = 2'. 8 = 2s; 16 = 2a; 32 _ 2 64 = 26. I z , 1-=2". !=2". t ".. 1 2.. L=z-. 248163264 418. 1) (-8F ( 1)r'= 64 1= 63; z, sl ?l' =s. a =!.t 9l al I gr s'' -a'=! 1=!,3412 4t 2" +6" =1* r = 9 * 2 =11,a36727272 srlll +t-2.:f s' i I '=8,5+t-0,04 4,46; t7/ 2 25 6)9.0,1 '=9.10=90. ::iiti::illtill: AITEEPA Mep3nrK A. r. ra iH. AKaaeMi,{rinn pieens f! , a=!;+31 s v = ilii2: +1 y =!2 x; 5 a=C4-z; ol y = {rl. 416. 1) y=-Vir; , g = 4lci;
  • 419, l) a1 ar atll 2 tt1 : a5 = a': 3) (a15 = o$' . taJ)d . dl di3 . o4 tlt ---.-iE = -;-=oI 5 {r5 a3=azl 6) a' ato otr - a 1: 7a-ttat5=aI' 8 ar' a'o i ae = a12-2ite - a' 9) (d 5)a = a 'zo; 10) (a,) a (a,), : (a-313 = a3. a6. a-24 - a3+6+21= a22. 42O, 1) 2s. 2 1', 2 " = 2 e ',+" - 2 2t..r.111 =' : =21=i.l' t3i t,4)=2"=L, t 4t9t.27,=33 36=3':;: , ?, r,3,'1" 'zs,'rl25r' 9 125" 9 9.9! 5" - ^,, ^,.t)['oJ llr] I'ltl t27)-% 27' sr{ -;ii 5r:J- 33 ^. 226.23 2" tl' 23 2' 16 u, ;;r",l-fr," -to--"=2 t6. 6. 8r3HaqeHHr ra E acru8ocri creneHt 3 paqioHatbHl,lM noKa3HtlKoM rr r ^^^.i^r a 425.1t 4 =J4=2t 2t25' l2b': 31364'-3'=": :, 4r -5 0.01 = 5.' I 5.r00 s.Jroo'--s f ooo ooo = -sooo, 100,/ lr z1 au =Ja': 3l b - ';: !D b) t..b) = a oi Gi: 6t ob' alb'l Ed ro ^r "a sr o.rz; i .lloool' J/10" 19 loo = l r25 ,r 'J 5' 5' 25 er lnTl"=li?91"="/tP'-l3l' 3 243 .ts. 64) 64,] / 64" 2/ 2" 32 32 427.|t y = t6, ,(y) = t0; +-); 2l v = t La, D(g') = (0: +*1 3' u = k - 3)L6, D(s) = [3; +-),60 jr 3 >O, '>3;l 4) a=@'z-6,-71,, r(y) = (-*; -1) u (?; +-), 60 x' 6a 7>0. .? 424.1 s = x', ,(y) = (0; +-), 60 r > 0; 2 y = a3,, s = ai, ,(y) = [o; +-), 60, > 0; 3) !=lx+11 "rC ',-Dlll tl: r-).60r-r.0,.r.-1r (r + 1)it 1 4) v=@'! x 30)6, t(y) =(--; -51 u[6; +*),60r'?-t 30>0. o, n.r,o i = ,/]!gq = ro = 1= r?.' 1216 6 3 3 7) 27, =:127 = t127' 27 =27 3=8rl 426. r) 8: = J2" = 2l !- 2) 10 000' = l/10' = r0r 3) o,oo81 o'5=(o,oo81)ii =(#,)' /1; tt 1 =4, =,143 =23 =Al 4) tt! 429- I) a' d.3 =a6; 4' ao6 . a5 = aa,. ??1 7 ai i |la, = az : a6 = a1r. 7O at.aE.a3 =aa'aa =ai. 1.. d"o" - ';r ^D ^i.Lzt _l_4 .? ',l':J '={#=;, ", "r".=[ t l'=Jt =1 32) 32 2 / 'J : t: : 2) a,J ob; 3) d, ta3.-a? , -a6l rr (,"/ tloi 6) a a' =at a'=an 1 -! l,' ill 8) (a '.14 = a1.', 9 a3 iaa =a3 a = a3. 11) (ao,)o 3 / r !i r ! 13t a6 b,1J =a, b'. 421. 1) 53 = trE 4)106= +--l v10' A1 6 -es1i = 1y 3y1a={1r 39tr. 11 422. tt t3, = Jlsi 21 3' = ^t, : 3t ro' .c' = Vc: v3 o :1 -ay x " lx6; b, BnrLno' 3m,n, =3{n'n": 6) (a. - 2bli = 4t" - zt'1" . a2s.D yli . x 2) ta" =oi; , 4) V3o (3d)'; 5) ,12'" =2"1 tt llto - tt . t" ot", 8l Vr- b' = {d - b )s. az+- t1 Jz =2it 2 -{a" = ":l 4) Vbo' = (5a'); 56d6: 5) i/r t y tx - stt: s) V6u = 6'; e) ,1[s = 4e'r; ,! 3) ns =n u el 'i6F = o,ai. illl:lfi!*illl UTESPA MepstqK A. r. ra iH. AKaAeMi,{Hr.rn piaeHu llt: 3Zg328 !tl: AflTEEPA Mep3neK A. r. ra iH. AKaaeMi,{Hnr piaexu :illi:il:lill:i:i:l
  • f t4 o: . o''" . "2 . "; = .; ;'i: = "' lot otl . lo 6/ =,' ,'". 43O.1) b3r 'bL'=boli a1 t,t: =6"s =6i; f ?" ! 5) l6',l = D',: 7) lrE tb 6 =b.'6 =bE =bi' 8) g)o b, o 6t o"i6- "=ai 6-: 10r al o'' = a' 16 . bt'i = djd . ba. oi bt / ", r L 12) o "b, J = arb 3l 14) (6o6f 5 bo.{=bo,3 bo,r-b01. 16) (b1){r : (b o,a) 5 = D '3 .b1 b43 :; lzs"/ =1./ =s' b i .bi =bo -1; 111 i b,b1=b 1=b4. bt.,lb=b,'t=bI. bj .b a .: :,:'-.'_=o'"'=Di bt r oto.) =a)b'zi 1'rt,t,!13 1A) b' .bt b1 =b, 3 a =b1,. 15) (' o3f . (bo.3f.{ = 'i.3c b03' bi.o4. n, ll I " =,2 "t " = 7' =B4B: 491 ..'-6,' . ... t20,,,zi ,zo.t'bt 12") 1.4' -l;l l;j =l.:r.J 4, .t4'=J2Lo 2" 22. !! 4,8f 33_":j-". a, Bt 7) aD4.2t3 =2t'.21.3 =23 =A I 8) (6r3)a.2160,-606.(64f,=6i,G 60,6 - 60 ,1. 2') 4) 6) 433. a > O, r) ('6)" 434. m > 0. I) m =lm")'; r / r)' 5) a, = rn,/ I 435. b > 0. 1) ,6 = (b':)3; ar = ta.l : ," = ('"-/ ; 2) b15 = (b t)3i o ,i = (6'i,) , *'=(-:)' , v = (,3)', a: = la"/ ; zt l<,li)' , ar (Jo)"; ,1r (Va ) . 4l 8) 4',) 8) 3) 7 3) 7 2') 6) 431.1) a" srd 3r3=J, =s; 2) (503)6 54.s-5!,3 5n.3=50=1; ( r), ," ^,1 +sz. r' lars: f-ll'l r, , "f =7, 7 . 7i I t49.r / '''2) t0" 40i.5- .lot ]oi 2r S, l0: 2? b = I00r t0; 31 0,0016 4 0,04 ^-0,216 J t0.2', i-fi0.21)-, {{0,6)') ,- o,2'-o,2' +o.o' { Il -t*25 tzs s*27.-tzz1,.125) I I I 4) 625135 255 253 =(5{) { (5'9t5 (53)t=5' 53 . 5' = 5 3 . 53 = 50 = 1. .. 32"1.4o- e'f 2t1 2t,.2t4 Zb ^, I 'r 640'.t64?" (2')q(2")"." 2L6 |=2h-z 4i ^ t2 3' 7d 3 .2.3 7s 6) -- r'" z' .8-' I , ! l" t' |513i, | --t"? ^"-s' 2,.2'-zs.s:zse-2^ll: frr; z;.J ' 3 2 256 ll 11 r: l" I r r, | 8r'.8" | .l 2' .27" 33 21 | . 2'3.3'n "'l;l;l l,T,*1.] L,I;l ,,: ,; 3',,,2" 2-3, 2, =L.729 b) I I J r,2" =t1,2t0 .1,20' t,2r tt bJ o'l'll.l i 1l-,ro1i.,roo,j l'o.rooll e,[ooo = ro: r0/ l'7001 7./ .17 ) ,,e:=i="ii=r, 2t 2' 8) 3601 . 6" = 60'3 . 61': = 6': = 36; / r16 / '16 e) 14 "/ .16"' .2") z, 2a.4.2,.4 2, - 4. 432. 1) 53.' .5 r'3 .5 ': 6 53 ! t3 'z.6 - 5n - O,2. 2) (7'orrl t7 / afJ / a, B) le?J = s,/ = s: = 81; lr l |l =rreri = t/tc =z:'1161 33o i::::: AIrEEPA Mep3rrK A- r. ra iH. AKaaeMi'rHni piEeH" iallill:'::ji:.:: @6.2')" 2 3* iit;lii::jlllill: AITEEPA Mep3nrKA. r. ra iH. AKaaeMi,rHxt piBeHb iali: 3gl
  • a3s.r) I-; 0,04; .r,=(0,2),)r; l1l .tto,ztf, I -0.008: x=125: I,/ 2t rx-2t) = 32: (,, ,,i)1 ,r., .x 2=4i x=6: 3) (r'7 2.rr] ,, -L =-t.xea. lr" 2.r BiAnoqiAb: posB' trs: iB lle]{.ae. 499.1 t Li = 27t @ ti)ri = 27t, ,a = A2l 1 I .:c 1= 0,00001; .t = 1,00001; 44o. r aa 2Ob 4h - 5b a - 5b . 12ab 4 1ab 1ab 2l r' ,1 ,=tm.Dtm,_n+tt m_r. m'-n+1 m' m+1 ., m' mn mtm lnt ", tb,' _.J, - A(5, rlr) t' 7a' - a"b art1a bt ar =' b" _7ob" - be(b ra)- bs. ^. u'-t2!t-36 U 6f (6-s)' 6-go' te -, ={6-116. y)- t6 gx6 lt 6-g --- -. 5a+3 6-ga 50+3 6-3a (5a+3i(a-3J+(6 3al 2a 441- I I 2a'+6a a'.9 2otot 3) (a 3)(a.3) 2o(a t3)(a 3 5a'-LBa+3a 9+12a-6a' , -a" -g _ la'+g) . 2a(a+s)(a-s) za@+a@ 3)-2a(a'-9' a.4 4 ato 2 (a-4')(a-2 "' x. 40 '4 a' 4 a - 2t' '-"-2t--- a'+2a-a'+2a-4a+8 8 =-- G-8@tD = la-zr"(a+41 o, 2p 5 2p" 2ptp-51 _ 5V_jL | _ 2p' "r,.5--p e'[t p" p-s)pns) (p+5,{p 5r {5 pl(s -pr = 2j- :op -5p-25-2p1 5{p 5} _ 5 . - (p 5Xp+5) (p-5r(p+5 p 5' I u-8 1 1 ur8 2 -', 16-u" y-4 c c 4)ty 4) a 4 y'-16+@+qv 2aQ+4) a' t6+u'+8a-2a'-8a -16 16 --!J s v'l -ytty - u't= urt6 -n 442.tt(3c-t_3c-1.]. 2. g.'z 6. I g.':+6c-l 'l3c-l 3.-lJ 6c-2 {3c l)t3. lr _ 12c (3c+1) _ ]:2 (3c - 1)(3c + 1).2c 3c - 1' 332 iltiA'rEEPA MepsreKA. r. ra iH. AKaaeMi,{Hri piaeHb iLtiilillliiiii 2 I rt 2r tI 1ij=1ooi l(.r-r)iJ =100 t; 3) (,.-b)t=0; ' 5-o;r=5- (i rlzal1 r 2a 2l -- -:-=l-- l:ta 4obt4b'? 4bz az) a'-4b" .k-2bf t2b-a)t2b-at) a'z . ab'z _ 2b + a - (2b - a . -(2b - a)(2b + a : -2o = 1 = 1 (2b-a)"(2b+al 2a l2b - at 2a 2b-d a 2b' o,r d o o"t1l.o' a lota rl)-ora-1) a'-t ta-tf "'l, I-" r -i-71 ("L' -l' 'L a'-t) x+a a2 + a a2 + a + a2 + 1 . (" r)' = 9!l2g:))g_]I9) - @ + 1)' (a - t o' t o(d ' 1) (a lr(a + 1) a(o - 1, a(d - l)i a-1 443.1, abt + atb; 21 2a - aat +at = 2dt A 2a + a"bq" -6dasba3 -2a-saasbo3. (^i)' ("i)' = ^i "i (s,;)- (.:)' = ,,: -/, ? 1t ? a3 + 2a3b3 +b3. 4 (,r) _, 1,r,:.11,:l'=, _1,;_r,:.4 4 I 2 16 (aq4)x + 6Dq1 + 9 -6Do;' = Dd;3 + 9j (.t/ -r'=.-rr / ,' / ''a'l +a" I =a+a': r lt , o,-16o"-(r'-1s'"*25)=" -roda -ds - toa, - 2s - -2bi ! !1 ? ! '] l r ! 4 ? v ? 9 b5 4brb3 + b3 + 4b6 . b34 _ 4b6 /. '' , ,r), U"'l tb'/ .l("' a'l=1,' .6')6' -a")=a" -2a3b'+bx, ,,) [; _J[; -";.,1)G -1)=("; _JG.J_,; _'. 444, Ll L'a" -2oao4bo' +aD1bo' - 4ban = l'aas -tTao4boz -4bo1. 2) (nx''z - (no i)'z =n-n' / ,' / ,'z sr l"l -(sa ,l =a" -2sb'; tt 4 m 2m'12 + 4i 3 !? 1 ! 2 ! 5) b3 -2bcb 3 +b t = bx -23 +b B ttti:{iii:::::iil AITEEPA Mep3rqKA. r. ra iH. AKaaeMiqHri piBeHl tl:l i .i' z1 +n;) tzn-,n; $n.) 16n J r 12 + 9'i 5) 6) 11) 12) 13) 8) 9) 10) 14) -a06 - a') 6c+2 333
  • uv ('i)' * r' = *i * r, T v3 avr . aon +rca + gy'z = g3 8a'+16g+8a'=uz +16y; 1 ?! I a1 1ll 1 I I I 1 ! 8) c3 +6cscc +9a5 9cr2c1 6cec4 =ca +6c6 +ga3 gct -6cc =ca- s' {,,)' ,'J{,, - r)= {"1 r)i,; ,J=,1 -,, ,, ((":)'.(,:)')(,; Dt)=(,i .bi)(":-bl=. b qqs. rt 0,) lo',i -1,, -r'")1, ')l , (":)" _(,:)' =l"i ,2)("i,bi) , (-r)' [;)' =(-:-":X-i."]) ,) (,ii_(,ll=(,: al)(,i.B;). ,) (,:)' (,,1f =(,: -,i)(,t.yi,), 6) (2'L,, - (8s".* )" = (2'o., 3ao35era ' + 3v4 35). +ao. rr L:) lb)' l"; bll': -b') , (-;)"_[:)' =(-:,;)(-;.";). r, (,',)'-(,' | 1,,1 , -;1. ,11 o, {,,)'-{rl)'=(-i ,"1{-l "r:) o u-"= (ui)' ("i)' = (u; -";)(u;."1). ur ro,'"'y,(u,i)' =(n'",' uri)(n"'*-u,i) oor.,, (,i)' r(,1)' =("i *r:X":,:u:.o;), ,) (.,:)'.(b;i =(.;.ri)(,;,:u;.,;), ,., (,'*)'. (r':)' = (,.' * r*')(o; o':r;*r;), oon. rt (oi)" * ro|=,i Ll n r), o ,:b: _.,i0; _ "ib:("l b?), tl , s) '?i lm" 1/; '/ 6 71 2, zt = z, zt l; ouo. rr ,3(,i u)' /,' t ttt 2t b,I 4b'=b,b, all ll i '/, 4) c. _ci =cicr _il=".1.. rl, e'1zi .ai -31 =ri(ri J, sy "l(,1.f. 0, + 2b. ) at +*) ] l oi + atl 'l ' -rl-, tl +sr. rr ",'i -i'=o,r a' - r/ ^. a"la.+c'l .l (ai n .r/ I r/ r r r _ ldr - brlldr + b,l at b1 Dt ,l/r r = _-iT; a,b,o, + b1) aibi ,) ,l ("" I .6)=,;(.1 _6) ,, oi(, -r, l) ,i(, ol), 4) bq3(3ro; - co.5). " ,loJ.("' ;;-,1 1)=,:r;(":b; _1) u') ^;,;(^*^:,:,,). z1 1z"1iu - 121i = 2i; 2iu = 2i("i J = ri(r-' -,)' ,y ,03(ro3 * J. : a+la'(o + 1) = at - zbi.4) 6) 4) 5.) 6) 334 [;)'.r. =[; *a)(o aoi *s), ,"",'-(r'J' 1"" ,i)1"" -2:""' ,:) l"i,z"ll"i-rl'' r11. [;)'.(,;)' =(,i.bi)("! "?bx .b;). ::ii: AnrEEPA Mep3nqK A. f. ra iH. AKaaeMi,{Hhfi piBeHb :i;:::::::::;::::::::::::::: ,,1:"1 ,o,), =r": "0,", 8) ze za' ) o,')"-l';"I" (.;)' L,l h" .')(, ,'".' .) ^.^.;-, iillijilliiili; a,nresPA Mep3reKA. r.. ra iH. AKaaeMieHrfi piaexu i:ilr ggs
  • tl5 'o''l).1-ul=1,rt [x, 6J .r; ,l ' /1 t 1',la' r ?/. = ,_ ld' + 71 = JLi a,o, $l ,; _t),, _z) ,,_t _ ^ a' rt oi 6i(5; _ r) 3. 2l r2r:-:- -,,-, 'i = --__: = 3r. 2i.Ei _25 z, s. _rl 26 1t' +sz.ye!!!:-!.=ol. 1"1 . r) o I aro.t _to.|r = " ,"(.: 36) ,,;(.t 6)(,,; _ 6i , { : "lE) I , r = r L , m'm" +oii '1" n" - 6i tn'16 6/ r r : ll ! I ^. 8i .31 84 8. 13. li 2. "j 31 .2t _ 21 34 84 rl 21 ( 3), ou".,. l n I ' l -l t ' l (o -' ' (rvr) ll= 1,'-- - l.- .2, t ) 4 ,r u: -(S) ? =1r'fi *1"''"ri =zi ' z-" ,? u n",, lr r;) e')"^ l2i) " =r.o. -r'=z' z', t t / ' / ,': :r lzl-z')lz -z )=2,) e't' 2 -r'=i-i=i' 336 {liAIrEEPA MepsreKA. r. ra iH. AKaaeMilHr4t piBe*" iiiiiitiii:$il:! t r i t tu r : r r ltu i,.tr+Fa.3, l31 2t-8, 24 IL - - - - l- -, -, I =225+216=441i 5,+3. I ' 24 -3, ) t t tli ,t6 ,, I r' ,r'lr" -,e'I - (rl)'(rll' = B" .8, . zb s 22si 1 1s' +e"J ) rt,' r r r/, rr,d ", s".z la, z.lJ s,.2,24_3;llzt , , -r- = -, , ,, | 3' 2'=2'1 8=216. I lz,"g.l I t [2;-e.] ) o"n.,, tlr -ao'rra"5 + aq') _ (au' - r"") (ao5 bo5Xd+dorbo5+b) (ao5 btr5Xaor+Do5) a + 2ao.5bo.5 +b-a_ao.,bo.r _b ------;t' . b* 4ss. 1) ^r ,i) . n mini - na - ms + min - ni -- 2n.nit ., (ao5 bo 5), + (ao. + b" "1. - 2(a+b). a b' e :2!::!:t!r ! :4i!: ! 2a + 2b / , / ' ar -_tllai*tl .1, _ir;) j =b'" _1.1 b,:" 2. t,ti il .r lr, 2 /, ,,/ 11/ I !l "' ul ',",-a") la' -a'lla, a" )a" ' ai) "' T;l - 'r 'fr= ,ii ri, a6b;o' -brl t"a, -t') o,b'or brJ.b" . G o',)"-'lu,-o)G',-oi)' '',u; o) a'(a t)i.",', @-ar! _,, orl, -,'.!', - u)1" - "',0'", u=(,,, r, ":rl)(," . r,,,1r1) a'to - Dl a . tt - liui)' = a" + 2ab + b" ab = a2 + ab + b' . - ao'5 + bo; ; (,1 .blX,:-ri . .. / ,/ ! ,,,, (,,'")',tz o':ltz.'_o"t 1 o1",2-o',=s, ' 'i) ,, ("t ,r) l ::l=!:-4),; -"('l-bl)"; --"" I ,:b; _"bl ,1r(;^_",) ,(rl _,1) b' ii:litlitil:jl:t A'TEEPA Mep3reKA. r. ra iH. AKaaeMieHnt piBeHb t:!li 337
  • { . .1,^ ,, ",1(t'-",:) (.'-t)(,,i .r) r ^i+t-t ^L I '' ^;Gi) *(,,- ,)= .l^: ) 456. ltCrporqy€Mo iiBy qacri") roroxHocfl: ( ^"."' ,?+,)l?l : : i-'=n'm': m, +mn, mt+nr) , m'+n' m n" nt mn n(n m) ' J.i ,") .,-,,,= ,G:-,) =.F_,,)= "("i ^r(":.^t) ,("i ^:)= f t-lr= ^mn' + n'l I : : - nn' - m'1 m .. - r/r.. aoBeaeHo. 2) Cnpoury.vo iiBy qac.HHy roroxHocri: I ^a.s - ' -o5 ol ".2""'n a I l;d',r-d r' , ao" t2 ool z a ao t 2ao ' - 2 - la + ao ' - 2ao' - 21 - ,oo' - t)':(do6 - l) a+au" -2-a+ ao" +2 (atr" + 1l(oq" - t) (a05 + t),(aoi - t)' , zaa" -(aa" +11 2 2 ., " (aq5+1),(aq5 -1).a05 - (ao' +1Xa0.5 -1) a-1' 22 = . aoBeaeEo. 3) CnpoqycMo riBy qacrxEy roror{Hocri: t, I oJtt., I I oi+bi oit; "t-tI ad b3) o3tarb'tb1 ar bt 1. 1 a,bt at asba b3 4) Cnpoqycxro,liBy qacrrHv ro, ol+rHocri: h' z"a + a') ' r / ' / ' ' a. t,)a - a:b, - bl at + t- la + a-t- - ol o, a'b, 2aJb 2ab2 | o"b2 - b- - a, - a,bi - a-b + b I tt l (0 bJa + alb' + b) !??lq:1 _2a, 2a,b 2ab, + 2b, 2a, (a _ b,) _ 2b,(a _ b,J -l b blla t oii t tl n btla - a-b + bl t r t/ , z"' *)"+"1t'+r) tttl 2a' _ 2bz. 2a' _2b' 1". "!ri t u) AoBeAelro. 457. lr I. - + ---:-=---Y- -' ,,t ,t r ,/ r rl ,'u,,, _c I r's ,(, .v,1 2lt + D I1 t 2xiy'+a+r+2x'a'+a t,t t r/, , x,y1x, + s,lx, a,l c 2rx - ut Ji - zr' , yr ''.i. 1 x;y;1r.- s) (2t + 2s) :,iai(x y) z(r + 0 ' a pi6no"i6o. L. ^. . irt + 3y" xG - 3y6 lt r'/r LlLj! ! l-" ..;l la6 -,6Jla6+/6,v v1 ! t ! tt I I 11 11 1 _ t3 + x6g6 +3r6a6 +3a' + rz - t8gi -3tiv6 +3y3 ,:)'(;.,;) I t tl 2 2 l" " _a "/L a 1o 4 t 46 t) i-----i = / r- a 3 -r 3 (,-r L/ ' ' brlar+a3b3+b3l 2 I t' |,,t"7tL , _ la'+b'la3-o'b"tb,l _ t _ t _ o.b. ' t t tr/ I I ! tl , ?t- | | - I 1 - a"_t"lo3 axbitbtlortb,l b'_a" a,.bB tl3b3 arb3_ = _. AoseaeHo. 338 il::: AI|EEPA MepsncKA. f. ra iH. AKaAeMiqHur piBeHb ir:iili:::iti;:l:..::l t, ,,"r = 19 = ?, 459 Bidnoaidt: !: 0: ?: 99 2) P(B' = Ol 10+20 30 2 4t PtDl=-=-=-.45453 2 i 2@-.'G1 -bi) _ o-ttGtoii tt) tl = 2a' - 2b'z . (": - ,(,1 t"oi) - (,; - ,;)'(": ., ,:)' ,(,1.r,;)(,;-,;)2- +I t r'/ ' r/ r r l*. - ,.J 1,.. + y.J(,. + 3!.J BiAnosi}b: -: t, ,i -ai tsa. t, PrA.r=!1=?9=!,'n4ng i::iiiti:iiiii::itl AITEEPA Mep3rqKA. r. ra iH. AKaaeMi,{Hun piEeHb Itli 339
  • 45e. 1) P(,4)=#=*; 214Biilnnaidh: 15 lo t5 2r PrB)=a=1.30 10 A4 3l P(C)=:=-.30 15 46s. E;1 = {i - z; 2, - 7 = B - xi s' = 4i Bianoailo: !. 3 D J%- = Jr-'2x' lrnepeBipRa: 1/2 ; -1 z Bi)noatla: L. 2 s,Ex r=J;-.2x-1=x 3i2x x=-3+1;x= 2. rrepeBipKa: J, e>1= J 2 3t Ji = J- - "e .ae sl'i"'y. Bidro8tAb. HeMa€ IlopeHiB. 4).,8"-1=tlF*sr 1s; 2, 1=x'+4x 16ir'+ 2r-15 tz= 3' IepeBipxa: x1=-bi G11 =J-11 - ue uae euicty; .rc, = 3; .fi=.'fi Bi0no6iAb:3. 464, 1) V.r-3 !,12x-3; x-3=2x 3t.r '6; .r=6. nepeBipra: {6 = d, - npeBr.L'rLgo. Bidnoaidb:6. 2) fi* s=r6lxr,r,r s r'r:S*=O;x l. l6 l 6 "=l. I FcMA{iMicrv.nepeBipka: i4 ; 5 {r ,, i-t I b BiAnoaidb. nopelliB HeMae. 4 tlz" -zs =V5;+10; 12-25=2t+ 10; ''-2x-35=0; x= 5;x2=7. BiAno7tAb: -5t 7, 4 F-s6=J2r-1) "-36=2' 1; x2 - 2x - 35 = o: , = 6;x2=4 riepesip(a: ', = -5; rlEb-36=J-10-1; J-rr=J tr ge uae auictvr r,= ?; Jta "{l - npaB}1r'1,,so. BiA o6iAb: 7. a65.1 J2-r=s 2- t=t';x'+ r-2=Oixr= 2,x2=L flepeBipriaf nr = 2; J4=-2 - aenpa.afl,Ho; r,=l: u4=r, r=r npaBunbgo BiAnosiAb:1, z1 .lz+ t = x - 1: x + 1 = 12 - 2x + !; t' 3:. = O; x(r - 3) = 0; r, = o; a, = 3. IlepeBipria: .r1 =0i 1= 1 HerlpaBrrnbHo; x,=3;2=2 - npaBl'rn6Ho. BiAnosiAb: 3. s, ',h; 2-,;3,-2=)rx2 sx + 2 = oi r' = It ', = 2. IlepeBipxa: tr = 1;1= 1 npaBvnt']jo; x,=2a2=2 trpaBxJlbHo. BiAnosidb: li 2. q Ex'z -Sx . 1O xi 2x" - 3x - 10 = jzi x2 3x 10 = 0; jr, 2t.x, - 5. r€peBipxa: t, = z; rETzt' -a C2t 10 = -2: 2 = -2 HenpaBu,!6Ho: .r, = 5; $.!'1.5 16=1 5=5 rpaBr",l'o. Bi0no6iAb:5. :ilil:.:tilllilli AITEEPA Mep3ncKA. f. ra iH. AkaaeMiexr,rr pieelts i:i:: glr 4 460. Hcxaii y tiopobui r.6innx KyrboK, y.horo (r - 25),ryn6ok. PlAl m = L'''- n x-25 rrro ra vMoeorc ralaqi c."r"r"t" ? Mscvo pisgrgns: * --li z, =2, su;' 7 a-25 7 5js=50;r=10. Bi0no6iAh:10. 461.1) J2r.-l =21 J2r-l) =2'i 2x 1'4t2x 5ix 2-5. fiepeBipra: .,lz z,r-t=z; ,!4=z; z=2. BianoeiAb:2-5. 2 lx - a -2i (i/t-4)" =23; r - 4 = a: x = 12. Bidnosidb: 2. 3) Jx-6 =-3: (V'-e) =t-3ti! 6 243i x 237. BidnBidb: -237 . 4 {," -2,+s=*; (1t'-r'-sl =li 's 2'+3=a3: 2r= 3;x=1,5. BiAnosiAb: L5. sr lz*fi'*z =a; (]z. G'.2 ) =s"; z +{V* =s; ",,F * =z; x'+r=a; xr=1:.x,-.1:r,.1. lepeBipnai t, = -t;,fi * trEi = s1 ..li + z = l; 3 = 3 - rpaBrlnr,Hor r? = 1i q. tllJ 3:i 3 - npaB,nbEo. Bidnosidb: li l. 6) Vr'+rg =21!*1; f + 15 = 8(' + 1); " + 15 = 8' + 8jx'-8r+7 = O; '=1; BiAno'iAb: i 462-D $: 3=at ("[ r)'=n', '). 3=16;'-1e. flepeBip&a: .,its s =a; u/ie =n; a= I * "puu""u"o.BiAnoaid6:19- D .'lSr' x 15=3t 3a' jr 15=9; ga'' r 24=OtD=289 8 x1= i x'=3. .--8. /" 6{-9-,o=3; yfn-rs=a: a a EpaBx,,r,Ho:rrEPrirPnd','.-''{"'-;_'" x,=a: JB.9 a rb ai Jz? 3 rb 3:3 3 npaBlnbgo. Bianoeiaa: 9: s. 3 al i6s -G' * s = s, 2s +,,lVi = zt. n[V * = z; r' + 3 = 4t r' = 1: xt = r, BiAnogidb: 1; -1. 34o lal: AITEEPA Mep3rrK A. r. ra iH. AKaAeMi.{Hrai piBer" l{i{litiitial 2r.-l=1 2ti4r=2; "=j. = 5 .lrt o = o - rpaBr.rn',8o. =0jr,= 5;
  • fi 2@i=x+2;4(r+ 5)=(t + 2'i 4x + 20= t2 + 4t + 4t '2 =16; rt- 4; IlepeBipKa: r, = -4; 2J4+5 = 4+2i 2= 2 Eerpairn6Bo t"= t; z,ln+s =a+z; 6=6-rpaB[nbHo. BiqnoqiAb:4. A1,!tS - Sr - t = x; J15 - er = x + t; 15 - 3' = (t + 1'1; 15 - 3t = x' + 2t + 1l t, + 5r - 14 = Oi ta = -7; r,= 2. nepeBipxa: xl =-7; 1tl5 - 31-1 -1 =-7: 5=-7 - HenpaBrnbHo: x,=2i2=2 BiAno6idb:2. zl , 'E't*-zt s;, s $,' ,-aix 3)!=2xt ' x-2t ,z 6'-9=2zz+t 2li12+7t 30 = 0; r, - -1o; r, = 3. IlepeBipxa: r, = -10; -10-J2(-10)'+(-10)-21 =3; -23=3- setrpaBr{nbEo; '"=3i 3 - Jr./' +3 -2r =3;3=3 - rpaBr{n'Ho. BiAnoqiA6:3. el "tz.',18 3, "" =o; u6-g" "'=-t'+2): a 3x "=(-(x+2)r'i 8 3r-r? .r:+4,r +4i 2x'z+7x 4=01 D=81: ,,=-n, t"=i. IIepeBipKa: t, = -4; -4+2+ J8 + 12 16 = O; O = 0 - |*r*fi 91 1=o',=o He'pa!&r6'o. BiAnosiAb: 4. 466. 1).[0-3r =-r; 10 -3r=.r'; r'z+3r-10=0; h=-5x,=2. fiepeBipxa: rt = -5j Jto*fs=s; .85 = 5: s=5-npagurEHo:r,=2: G=-z; 2=-2-EenpaBrrnr,Ho. BiAn%iob: -5. 21 x=Jr+5+r; r -1= 1G *; 1 npaBunEno; r, = ; x' - 2r + 1. = t + 5i t2 - 3r - 4 = 0; r, = -1' di=z; r=ta. -t = 3 _ HenpasunbHoi.r" = 4; {= J9-1; 5) '-!6;'-11a-20 =s; '-s=6"-rri 20t x, rox+25=Bt,-tla 2oi 2r', - 45 = Ot D = 362i = 4,8; x,= g. nepeBipka: 't = -4,it ,4,5- JA(-4,5, -lr.(4,5)-20 = 5; -14,4 = b Henpa, llrnbuo; r2 = 5; 5 -v6.5' 11 5l[ = b; 5 - b - npaBr{nLno. BiAnoqiAb: 5. 467. 1) G:r+1= 0; G-z = 1; 3a BlragaqenEsM apreMenrqEoro RopeFrs Jr 2 > 0, orxe. pisHsHs' Be Ma€ xopeHis. 2l Pli+t"lxt=-2, sa BraHaqeBH'M apr,abMenrqHoro RopeHs i6>o; {GJ>o; cyMa HeBiA'€M[r,rx q]rcen, .rjrcno HeBiA'€MEe, orrne, piBHfinHs He Ma€ Rop€niB. s) ,&J-Jf -.r =5: oAs: 1x-4>o' x'4' 1t - t - o; ]*' l Po3B '3KrB seMa€' PiBHtHHt He M6. konaHiR l- a- a) Vr-6, Je r l: o.[a: r- '-0' fr>6' r- 6. 16 -.r j 0i ljr < 6r Ilepesipxa: 1f,11uftl = 1 6 = 1 HerpaBurrr,no, or'{e, pis'rr'n, He Mae s) .,60*"6*r =r, 26+Jx+1=zit .,&*r = -r. piBIIssHs ne Ma€ xopeHiB. 46a-D {; +zda' -3 = o; aai.{isa: {6 = r. t+2t'-3=0i2t'+t 3=oiD=25jr,= 1,5; ,, = 1. {6 = 1,5; .r=-s,3?5; Vi=L ; = r. rlepeaipxa:: = s,azs; iFg,g?5 +zifi a,gz5)' s=0;-1,5+4,s-3=0;0=0 -rpaBanbno; r= l:4I+2a,Ei a=o; o=o-npaBnnEgo. BiAnMiAb: 3,375i 1. zl G+iG-a=o. Ba:uisa: i6=r; r>o;,4=(G)'= t,i trri 6=0:t.= 3i !r=2. :3 I{e saroBonl'ns€ yMoBy t > 0. nepeBiprca: ", = -1; -lJ-t+S+t; 4=4-npaBsnbHo. BiAnoqiAh:4. $ nEr 5, * a = Zt + 2', 2* + 5t + 4= 4x'z + 8x + 4i 2r'I + 3t=U tzt + g)=O; .r, l,5i .r, 0. fi€peBipRa: ,, = -1,s: Ez,zs-z,s*s =-3+2; 1=-1 - EenpaBunbEo; r,= 0; 2=2-npaBvrll,',o. BiAno6i0b: O. l) ,'+tO-rt=Zr; a,&l tO = Zr + tt; 9(r + 10) = 4r, + 44!+121t 9,r I90-4,rr t 44x t l21i 4,r/ - 35-r - 31 OiD.72gtr,. .t; r, - -4.'4 nepesipxa: r, = -l; Sv6-ll =-2: -2=-2 - np"urronor r, - .91, ,[!l-,o 11=-?1, -11=-!1t 4 222 BiAnoqiAb: -1. 342 ::tt: AIIEEPA Mep3nrx A. r. ra iH. A(aaeMi.rHrr pieexu !iliiiLi:!!:;:ji nepeBip(a: +6 + ri/i6 6=o: 4+ 2 6= 0; 0= 0 - trpaBr{rbrro. BiAnuiAb:16. 3) 2r-7J; 1b=0. BaMil,a: Ji =t, t>o; , = Qi)' =l; 2t, - 7t - I5 = 0i D = 189; f, = -1,5; r, = b. -1,5 H€ sa{oBonl,Hse yMoBy t > 0. Ji=s; '=zs. nepelip(a: 2 25 - 7nE5 - 15 = O: 0 = 0 - rpasr{rEHo. BiAnosiAb:25. ql !; + el'G = t. 3ardsa: VI = r; t > o; l,[r = t": tr+3t 4=Ortt= +ra=1, -4 - Ee 3aAoBonr,Hs€ yMoBy t > 0. G=1:,=t- Iepegipka: {/i+aVr=l; I + 3= 4i 4= 4 - npaBunbgo. BiAno6iAb:1. zG-t b a-. Bauiea: Jx+t .r,r.o. V.r+1 i:iililrillt::l: AIrEEPA Mep3rel( A. f. ra iH. AxaaeMiqHxt piBeHb !i;l: 343 I I
  • 3 2t-5='i 1t "- 2 2t'z-bt 3 o. 2t, t 5 !7 - 5t - 3 = 0i , = 49: t,.,= 4 ; tr=3; -; He sa,qoBonbBn€ yMoBy i > 0. 1Ci =z; r+ 1= 9;, = 8. IlcoeBioKa:2v6*l -5- ,3 ; t=t-npasribHo. J8+1 BionosL1h:8. o) "'-r+g*nf'-'+s=12.3aMiga: ,lV -t*s =t, t>o. t,+t-12=O:tt 4;t,=3. -4 - se saaoBo"'1l,Hse vMoBy , > 0. ,Q -a+S=S; r'-ir+I=o;.tr(t-1)=0; 't=ot x2=1. nepesipRa: r, = 0: 0' 0 9-19'-0-g 12t 12= 12 - npaB,lEHo:,rr = 1; 1' - 1 + 9 + Ji' L + I = 12; 12 - 12 - rpaB'r6Eo. BtAno6i0b: Oi . 7) lrF -+'*t 2:!S--s=o: :lA4 - z{;- a=0. saMilra: {t--t; t,-2t-3=Utt-3itz=-1. {x-z=s; x 2=zlix=zgi V.1--'2 = I r 2=-1it=1. BiAnoBiAb: L: 29. 8t -1 - + -3 2; oI3: x * l. 3a-MiHar iF = i: I 0. Vr-1 Vr+1 I 3 - 1.1,3/ 3 -2ti'?-ll' +--2.0: - -'.- 0! r-l ir1 (i r)0,r) -2t2 + B! - I z, St = O, [r1zr s1 - O. ft-lxir1) L(l -Jt(r rl)/0i [i*Lr/ Ir G= 0; *=0; {t=1,5; x=5,062b. t+1+3t-3-2t2 +2 BiAnoqiAb: O| 5,0625. s, .F-*z.F==s; oaa: r-1'o: x- ( -,!r-1 I.r+5 x-l /;* 5 Gl r saMirra: ixr =ti t>0: { . =-: (, 1Xt + 1) it=0:r=1.5. Lltl:f*-1: 5) u (1; +-). ---+---'-,,--+.-J-_-:_' ,,1,-8,. '' 7r- 8' o; li-8r- 7=ottt lit,=7. - l{OpernB lreMa€; Fl! =r, tt 5 as. x 5 4sx - 49 0. -48r ' 54 - 0. li,r-l rLI r-l I 8 Bianoeiaa: 1L. 8 l0) 'gf -1{' ' l, o,A3, x+rixt 7. Vr' t v*+t 344 tll ArrEEpa Mep3ncKA. r. ra iH. AxaaeMi.{Hrr piaexr iltlil:ilillli x+5 -r+1 6 - -=0: =(,r-l r-1 j,, =,:, l--t. {Vx ) r (V') -r I "r-' , Vr-1 ('[ l)(it-1) .. (Vr + rl (16)'*r 16*r=a;(u'E)'-trQ*z. q-o, ({,J' -+E z=o. saMiHa: i6=r. t,-t-2=o;tt=-1;t,=2. {x= 1tx I - Hc Ja,qoBo,rlHs. o,{3: Vi=2: x-8. BiAnosiAb:8. 469. r) r t 12 = 0; oA3: , > 0. BaMiHa: ."li =t; t>o, t'z. ! 12 Oitt-3t12=4. -3 He Ja,4oBonbHflc yMos! I >0; G=a; x=16 BiAno6i0b: 16 . z1 1w+8=sdi; Vr'-gi6+8=o. sardsa: i,6=r; t,-9t+8=0;tt=ltt,=8. {[=L'=1; iG=s; r = stz. Bidno6idb: li 512. g G - 4- = t: oA3: x 0. samisa: J:r i; t 0. i-"=0: : ' 0i tr-t-2=O..tt lit,=2. 1t -..1 - lre saaoBorElis€ yMoBy t > 0; '.lx = 2; x = 4 Bidno6idb:4. a) rt+5.-3{El;+2=o; oA3: r+ 5 >0; iu> -5.3aMiEa: d"*s=t, t>o; t, 3t+2=Oit,=t,=2. dG+S=L r+ 5=1ir=-4 dx+5=Z; z+ 5=16; .r=11. BiAnoqiAb: -4t 11. s, J- , , 2 I: olIS: n r l, -r , 27. 3aMiHa: Vx+1 Vx+3 I --L-r- o, t-3-2J:Z--JLL 3r-t+3)-0. /+l r-3 (lrl)0r3) lt+t-2=o. [t, r;t,--z- lt 2. Irr. txr.rt*0, li,-t:i*-a: Ji=r. <,6 =t. {r+1,(t+3) r>0. -z+4=4i r(r 1)-0; {i =-z; t= 8; i6=1; r=1. BiAnoqiAb: -8t l. ol i6 o'F*z{6 ,1 8 = 0; oA3: 3 - ' > 0, r < a. 1fi4-*y +2i6 "-s=0.garulga: &6-= t, r>0. t'z + 2t - 8= 0; t- -4t tr= 2i 4 lre sa,qoBonr,Hn€ vvosy t > 0; S-=2; 3 iu=64;.t= 61. BiAnoRidb: -61. z *'-t*a*nlV -r+q=6. SaMiHa: .,t; -t*t=t, t,+t-6=0; t1= -3i t2= 2; 3 He 3aAolonbEflc yvoBy I > O: G tt+ Z;,' i i:iltiir:lilii:i AITEEPA Mep3rqKA. r. ra iH. AKaAeMi.rHhi pi8eHb lt:l 345
  • r1 IlepeBipEa: ", = 0; 0'-o+++.,6'-o+4 = 6; 6 = 6 rpaBlrnr,Eo; r, = 1; f r+4+ J? -1+ 4 =6; 6 = 6 - rpaBsnbso. BiAnosiAb:0,1. *, it" *3 - lL " ,.r.613. L2 , e, I2.r-3 VBr 2 2x 3 E'*2 E*z r SaviHar -1"" --: = i: .l-'' : -; I 0. 2x-3 !3ir+2 t t t 5. t' _!1L2 _ 6, f' u -z=o. o_n. t 2 r Lt+o; - 1.. -o'1- 2"' - '' 10x + 11121+8-2t+3 -=ui 2x-3 3x+2-8x+12 - -=ui 2t-3 It=2.s. Ir + L5. flepeBipria: xr = 58;11= 15 HetrpaBrnbEo; t,=2i 3= 2 + 1;3 = 3 - trpaBtnEEo. Bi0no6iAb: 2. 2 ..8 +1- .,rGi=2; .,,6r*r=z*uG*r; 3r + 1 = 4 + 4.,611 + r + 1; 2x-4=4Jii; x 2=2Jx+1; r.'-4x+4=4(r+ 1); r'-8t=0; jrt,r .8r = 0:./, 0i xr 8. fiepeBipxa: x,-O;."E ."E = 2; O=Z o"r,put"n""o; x"=8;.lE-.tE-21 2=2-rpaBrnbno. BiAnoqiAb: 8. ' +zz. 'li-s +lEoi =3; uE s -s-u4o-ii x 5=s ou4o-,r+ro-x; 2v.24 -6',Eo - x; x l2 :vrio-r: r'- 24x | 144 gllo 'xli !'z tsx | 54 =0:r-=6:r, 9. rrepeBipria:;r, = o; ',/i+ ]a =s; 3 = 3 - rpaBnnbgo; l" .|*, - J) " o,u' . -r. [i"+z t ,r+z tt_= . -__=0: 'l2x 3 2 2x -3 a l?!t? ,. 3x +2 ^ ^.Vz* : - 2.r-B ' -' 5.{ + 14 [5x +14 = O, 2x 3 l2r 3+0r BiAnoqiAb: -1,Li 2.8. Ix = r,1, lr * r,r. *, o, "[ - '{ = ar a : npaslnbao. BiAnoqiAb: 6,9. zt Jxi t.!' t + fit=a.Jx t: 8.lT- = 22t 4J'l = 11; 16(t - 1) = 121; ., 7 - 16 - 818-1 +.:c 1; rcx=taz:'=#. 47o.| J22-x-.110 t=2: .tE -=2+.t!o "i 22-x=4+4J10 r+10-';i 8=4J1o-; ,Eo '=z; to-r=4;x=6. repeBipxa: Jzz s JLf4 - z; 4 - 2 = 2;2 = 2. BiAnosiob:6. D .l;i .rEx - 3 = 1t .tEi = 1 +.Ex - 3; x + z = t + 21Ei4 + 2r - 3; a, r = z1lzr4; 16-a'+a'=4(2r- 3)j.n' 8'+ 16-8r+ 12=0; t, I6t + 28 = 0. D = 744i = l4i x,= 2. flepeBipxa: r, = 14; Jl4,z "Es-e =r: -r t HetrpaBrni"io: r^ 2r "lr*z-"84 =r' 1= 1- rpaBr,n so. Bidnosidb:2. 3) ./E + 3 - G + 1 = 1; uE" * s = t + "l; + 1; zx + 3 = I + 2G+i + x + 1; 2x -3-2-x=zJt l; r - l-2vGJ: "r- zir I 4(.r + 1): x2 + 2r + 1- 4r - 4= 0; t' 2t - 3=O; rj =-lt )e,= 3. nppeBipKa: r, = -li J2 r l)r3-J-lL=li I t trpaBxnhHoi !,= 3t 1= 1 - rpaBnnEgo. BiAnoqiAb: -11 3. 4 2.rE- - 'h i=y uE-'=t+rt xi aQ-',=1+2$ '+7-' 8-4x-8r.r 2Jt x; -sx=2rt't:gx 47 x)tgx'z 4x 28.oi D = 1024: tt = z, '^=4=f . 99 nep€Bipna: x!=-2;2'E+2- Ji +2=1; 4 3=1;1=1 reDesio*a: EII.E ,=n/16 ,{ 16 3i6noui6o EI. 16 a) Ji-t+'t+1=r; "4-=1 ',Ei; t - x = 1- 2Jr + 1 + 1+ t; z,Gj = zt ri 4l r,r)=4.r, -4! 1.$t t,',=+, '" f .^ i E f----i:v.r L vlr l- vn n.nFRinke: r = : .ll +.11+:.1 "6=, - p=, ='; 2.f,-f, = t; -r = t BiAno6iAb: -2. qzt.tl .,Ex+S=Z+nlit: s; zx+S=+++nEr S+s"-s; A-r=a"lTt s; 36 l2r + x, = 16Gt 5); ,'z 60x + 116 = 0; , = 3136; r1.= 58.. x,= 2. 346 !ii: AITEEPA Mep3reKA. r. ra iH. AKaAeMi'{Hnr piBetb li::iiii-::!itiiii:i -_ft;lt; '.=-9,,/r' 1" -,/r-*-t HenpdBr.,bH.. '22Y2 Bidnoqidb: He vae HopeHiB. al'Ea -E + J" + s = s; nEa'at = t Jx. + 3; 13 - 4r = 25 toJr + s +.r + a; tO,G + g = rr + 15; Zuli + Z = x + a; 4(ir + 3) = r': + 6r + I : r' + 2r - 3 = O; 11- -3t ]d2= 1. fiepeBipxa:.,c, = :;.,4s+rz+J s+l=5; 5 = 5 - npaBllr6no; t, = 1; u6+G=s; r=r trpaBnnbgo. BiAnoqiAb: 3i l. a7g. Ja-r.+'E+5=4 J4-;=3 J:r+s: a-r=s 6Jr+5+t+5; 6J,+5 =u a+'+"; onGls =ro+zx; s',lrTs=r+x; 9(.t + 5) = 25 + l0,. + x't 91t + 45=25 +loa+ x.', t'+ x 20=O; 1'1- -5; t2= 4. repeBipKa: x,= s; Jl,+s+J-s+s =3; 3 = 3 - npaBlr,'lLHo; ,', = 4; Jl n *n4+s =a; g = B - npaBrrnEHo. Bidn%idb: 5: 4. 4 "6x+t+.,Fi=a; Jr"+t=e -.!2 7;5t+1=36-12Jl t+7 r; :i:::t:iliiiltil: AITEEPA MepsrtK A. r. ra iH. AKa,qeMiqHran pieexr il:l gaz - ,ro"uor""ol t, = t9;-9
  • 12li - x = 42 - 6r; 2.Ji- = 7 - xt 4(7 - x, = 4s - 14x + x'zi 28 4r = 4s t4x + i; )t'z lox t 2l Ot x, 3i xr" 7. flepeBipKa:,, = e; G 3 + 1 + J7-3 = 6; 4 + 2 = 6; 6 = 6 npaBr.rrlro; x,= ?; uEtz +t+"lil =a;6= 6 - rpaBrnb*o. BiArcsiqb: 3i 7. al J*+s+&+5 = s; .Dr+s=a Jx+5: 2' + 3 = g - 6$ + 5 + (.t + 5); 6J;+5 =g+ x +5-2r g; o'6+s = rr 4 36(r + 5= 121- 22x + r' 36x + 180 = 121 - 22, + x,t t, - 58x 59 = O; = r,= 59. Ilepesipka: x,. t:Jztz Jl5 3:3 3 - npaBllnbHoi.r, = 59: "E rs*g *"69*b =3; 11 + 8=3; 19 -s - HetrpaB'nb'o. BiAnoBiAb: -1. 474.1 x'-5x+16-auF -sr*m =o. 3a*i,.a: lEililili = t, I > 0; x' -5r+ 20= t', 1' 5x + 16 = 4= t'i t' 6r + 16= t' 4; t' - 4 - 3t = O; t' - 3t - 4 = Ot t = -1, tz= 4. -1 - se 3a.qoBonbFs€ yMoBy t > 0. Jx" -S,+ZO=4i f -5t+20=16i1.' 5t+4=0; ,1=lr,-4. IlepeBipxa: rr = 1; 1'? 5.1+16 s.'[' 5.1*20=o; 12 12=0;0=0-npaBrnB- IIo; r, = 4; 16 - 20 + 16 3.,[e zo+zo =o; 12 12=o; 0=0 npaBnnr,Ho. BidnosiAb: li 4. 4!'zta 5lx'1 2 0.3a,Mil,a: ,Tz r.t>0.x" 2-t'l x'=(+2 t, + 2 + 4 - 5t = ot t, - 5t + 6 = o; t= 3; t2= 2, uF -z =a; x,,2=s.f =11; r,, =sfi; .["" -Z =z; a' 2=4; a"=6; y,,=1uQ. tlepeBipKa: r" J6l 6t4 516 2 0i0 0: -r" uto, o=0, r.=-"fi, tt-4-5v[t-2=0:0=0: r,=Jtt, tt,4 bJt r 2 0i 0 0. Bianoeiaa: rll:l:r !18. rr 'f,'-r'* s * r'= 3a171 1t'- 3*-5 -.r -3.!.5 -12 = 0.. Bu*i.'u, G' -a"+r = r, t> o. t2t t , n.t - a.t 1. 4 - ne 3a,qoBonbnse yMoBy t > 0; .{," -e," G - z;', - zx - 4 = o; = 'rt,',= 4. nepeBipxa: ', = -1; VG1)'!31-1) + 5 +(-1f =3 (-1)+?j 4=4 npaB'n6so; x"= 4, J4' -3x+5+4'z=3.4+?; 19=19 npalgnbgo. BiAnoaiAb: -l: 4. at .,.6rrsrJ6=r2+8, tr2. Ba*i"a: ..6'iliilE = r, r>0; 1t'z-9t-26=t'' 3r' 9t 36+10=t?;3(ir' 3t-12)=t' 10' " t" to fi' lor 33 3t + t'z - 10 = 0; t'z + 3t -10 = 0; tt = -5, t2= 2. -5 - He 3aaoBonr,Hs€ yMoBv , > 0. nEt'-s*-,6=z; 3x,-g,.-26=4i3x, - 9r-30=0; r,-3Jc 10=0; r.,= 2; flepeBip&ai r,= 2: .FCI" g( 2>26=12+3( 2) 2l;2=2 trpaBur,so; 34s lilj ATTEEPA Mep3ncK a. r. ra iH. AKaaeMiqHefi piBerr l:jaltitliltllil ",=rr.,8.r' o r zo =12+3.5 5'i 2=2 - npanmrso. BiAnosiAb: 2i 5. 2,"+a,-zJV+st z =5. on3:''z+3, 3>o; ".1--; --3- J4,ur- " .E i .-,. saMiBa: uG.+3.r-s=r. r:0: 22 x'!t :.J 3 t;2x 6x 6.2t";2x'? 6x=21 - 6:2i'z-6-Bi-5=0; i 2t2 3t+1=0:r=1: t, ==i tr=71 '['",z, a l; x'':x : I;4x' l2r lJ=0; 24 - -t2 + 4J22 -s - ,lrt s .hc D: ll Tlep€Bip(a: x1= -4t 5= 5 rpaBfrlLlro; r"= l: 5 = 5 rpa8]rrlbrro. or J*,f, . tliT tz: 'rlx" t'dV 7r. tttii -'d'' -tz=o. Sauina: rVr3 =l, t>0. t, + t -'72 = 0. t, = 9j t,= 8. I ne sa{oBo,lEsse yMosy t > 0; 'V7 = 8; repeBip,.a: J:r,ztVttou * tEozE,ltou = tzt BiAnoqiAb: 1024. 475,1) x'-4x sn7 tuzo*to=o. sultri'u, 3!F - 4* + 20 = t, t>0. t'-3t-10=0;tj= 2;t,=5' 2 - He sa,qoBonbH.se yMoBy t >0; x2 4x+20 =5i t' 4x+20=25;x2-4x-5=O.1't=-2t x2=5, IlepeBipnai rr = 1; 0=0 - rpaBrnbHo; t:=5; 25 4.5 3,85 4.5 + 20 + 10 = 0; 0 = 0 - rpa3nnr,Ho. Bi?nosi1b: t 5. il z'{'" z,,n.4+3,r-r.: 2"8 3, lt" (r' srrll)'15. B"*i*u, .,frllllli - r, r>0. 2t=-t,+15;t!+2t 15=0i rr = 5;t,=3. 5 He sa,qoBon;sse yMoBy t > 0. uF-ar*rr=a; f - 3, + 11 =g;.r': 3jr+2=0; repeBip(a: ', = 1; 2.,[' - a . r * r r = 4 + 3 1 1'; 6 zuF-a.z+n=++2 2 2';6=6 npsur6ro. BiA o6iAb: 2. 4 Jr""-6'+40=,'z-3'+8. SsMiEa: J2x" 4, + 40 - t, t>o; 2r2, 6x + 40 = t,i z" ax + a + n = | ; "" - s" * e = | - tz, t = t: - n,222 2t = t' 24: t' 2t 24 = O: tt= -4i t2= 6i -4 ne sa,qoBon6lrse f >O:.lir'-Ar*+O =A; 2x: 6x+40=36; x'? 3x+2=0; x1= 1; 12= 2. IlepeBipRa: r, = 1; J2 1'-6.1+40=1'z-3 1+8;6=6 npaBvrt'Eot x2=2i Jr.2" . 6.2+40 =2" -8.2+8i 6=c trpaBrr'Eo. Biano6i0b: 1i 2. :tiliiltliiiiai AITEEPA Mep3ncK A. r. ra iH. AKaaeMi.rH!.ln piBeHb itair 349 x3 = (23)10. x=21o=1024, - 1; x,= 2. = 6 - rpaBrrbHo;
  • Bidno6idb: -61 4. Ir'+t-sruor<1. 476. f(r = 1, ' lr 1, rxqo x:1: l(') 3pocrae tra rpoMi4i1!&x ( -; 0l ra [1; +-); l(r) craAae Ha rpoMiniRy [0; 11. 477. A = hx + b - 3aranBEr.Ii Blrrnsa, MaeMo clrcreMyi | 2h+b=b, l2b=2. lb=1- lzr+a= :; lz**a= a: lr=-2. BiAnoqi1b:V=-2r+1, 478, V = at' + bx + c aaranr,Elri BLrrnnA, Ma€Mo clrcreMy: t tt' * tO, + .[r' * z" - tS = 123. Sal,liEa: '[V +zt ts = t, t>Oi f 2x-15=t''zi tc, + 2r=t2 + 15i 'x'z+ 1Ot = 5t2 + 75i5t'+75 +, 123 =0; 5t'?+ t 48 = 0i D = 961.. tt= 3t t,= 3,2. -3,2 ne 3aAoBonBns€ I > 0. J"+Zr-U=S; x'z+ 2r- 75=g; " + 2r - 24=O; at = -6t x,= 4 nepeBipKa:.r. 6i5 r-6)^+10 l€) t.//(-6,*11 6)-t5=123:123=123 npa- rrvnblo; x.2= 4t 5.4'+10 4+ J4' +2 4-75=123; nA=f23 rpaBlrnbgo. 4so.rr r.r r.G-4=6; oI3, {' l-9'"r. [.r-4-:0: u(r t11" + a; = o; (r - 1)(r + 4) = 36; x'z + 3x - 4 - 36 =0; r'z + 3r - 40= 0; = -8; ',= 5. Bi6no6iAb:5. 2r-3:O. 2t ,l2x +3 'lx- 2 3r OA3: i.- " x. O. x z -Ol 1@r+ sXt a=z; (2, + aQ 2=gi2''2 4x+3'-6-9=0ibe' r l5=o; D = 121, t,- 3t t,= 2,5. Bidno6idb:3. fr>0- 3) J). J1 r .rl oA3: i r.I0: Il. lxa! JrQ+q=x; r(1 - tt= 1 2 Bidnoeiat o. | . '2 r-t l2t 7-o- 4) ." - -Jr-4: Oll3i I x-4- Jzt 7 lr 4'or 18a+2c=2, c= 2, 9a+3b+c=10; {a lsI 4" a lr=, D=-a'+ t 2. t'93 lr=9, l3 4" 8 BidnBidb: U=-x-+Zx-z 47g. t) u =.8 t, t t .0, L* > o, lr x / 11 '= o' I'= 1' ''. (0, 1t, [x+oi lr+0: s = '[V-; )rs )e >oir.3- x=ot ..r:(x I.)=0:x=0rr ltrc [0:1]: 3) v= z-1*9,2--!*l'6.x+6 x-2 x+6 x-2 2tx-Gtlx 2 x,2+9x+54 ^ 2x +8x 24 x +2+9r 54 -^ k 4 6ttx 2) (n 6Xx 2) 2t'z+16x+32,r':+8ir+16 - l'+6)lx-2) -"' (x+6Xx-2r - ' tx-4t'z .o.r-{ -i 6)J{2:rF,. rr+6)(x-2) _at-_ ^olt , 2=.1E"'15.+28, x2 4x+ 4-2r2-15t+28i* 11r+24=O; x,= 3; 2r18. BiAnoeiAb: A. - t fr-s>0- 5) Jr 9 r./r= #; oA3: I ). 9. .h-9 lr>ui I' j--G-n, * ..9--6-"-9: e^ rs-0,9 15!l135 0' ' Jx-g x-9 jr I ' s 144 ^^ 15 BiAnoqiAb:9,6. et -!!:-J2x+s= Jr + 10: o.tr3: Jr+10 =o. [, 2 JiT-ts,rn=o. lzx -t z ot r+10>0. .r: -1.5. 2"r+3:0i foa-:a+r= s, 1" = 2. lgd+3r+r=10: 9a-2=2, 9a+3b+c=10: 4 I 4+3b-2=1Ol x-2 Ja 4x2x - 7) Jr' -, l 12 - 144 _j- J,r I0 J2,r-Bi - 24-x+tO=2x.3t Jr+10 -t+lt 1a!.^ , tz -- o, L'"".:tu .oi xt=-li.t" 26. '+lo t+to Bi0no6iAb: l. 481.1) ft2t + 3Xr -4) = r'4t (2x + s)(, - 4) = / - 8, + 16; 2x,-5t 12 r'+8r-16=0; rz + 3:t - 28 = Oi t. = 7tx,=4. flepeBipKs: r,= t;.,!1u+ly tE=-7-4t ll= 11 {erpaBlrnbHo; t, = 4; u@+a1a-a=a 4; 0 = O - rpaBEnlno. BiAnoaiAh:4- ::Itl:a:ttiil{i: ATTEEPA Mep3nsK A. r. ra iH. AKaaeMieHti piBeHb :::::;: 351 I i I I 35o ii:i: AITEEPA Mep3ns( A. r. ra iH. AKaAeMi,{Hur piaegs !ii::l:lillril::t
  • z1 1@ zyz" 11+z="; ,ft" - s' + to = r - 2, 2t' - gx + ro = x' 4x+4i r, . 5r + 6 = 0; xt= 3t t2= 2, flepelipHa: ", = a; "G ztto rl+2=3; 3=3 rpaBvnbHoi ',= 2; 1@ 2yt - s1 + z = z; 161-g a 2 = 2; 2 = 2 rpaB,,nBiro. BiAnBiAb: 2: 3. al O*zlJr" t zo=a"+n; O+znlVl"-m -6('+2)=0; Ir 2 o, lx 2. tx-2)lJ.r' -ir-20 -61= 0: l .- l'l x' x zo 6t Lr' -x-20=36t lx= z. x=-2- I ^ lx=-7'x" x 56=O: I lr=6. IlepeBipKai x= z; ( z+2)Jl+2 2O--12+12 O J-14= 0 - HeMa€ BMicryi x = 7i ( 7 +2J4s+7 20 = 42+12:, -30 = -30 - rpaBnnbEo; ;r = 8; (a + z).,6a 810 = 48 + 12; 60 = 60 - rpaBrrnbEo. BiAnosiAb: 7,8, .lt t' + tr,F - s' - s = x - r: tx+l)(Jx -rr..5 l) .0r l' = -t,lir.l U, x I. I | _ tr I, lJr'? sx+s=l: x'-5.r+5=1; I '' 1"-4. IepeBipRa:, = -r; (-r + r)rf-rf +:+S = -1+ l; 0 = 0 npaBr.r,rBrro; x I: 2vl 5-s 2: i = 2 - npae,{,rsHo: r - 4: 5Jl6 20 5 5i 5 5 npaBx,rbHo. Bidnosidb: -l|' l;4. aez.9 'lt *,.J, zt =,*t; t*'.[V*u= 12 +2r+1; 'Jit24=t'*2t: "("r-24-*-2J=0, l' o l-. o^ l'=:' L'lx' zt xt2i x'-24=x -a"r'a: lr 5. rrepeBiprca: , = o; Jr * on6; * z+ = 0 + 1; 1 = 1 - rpaBrnbno; , = s; JI;;J%;A= s+1; 6 = 6 - xpaB{xbdo. BiAn6iAh: Ot 5. 2) E;;.8= = ' t;1+"'["' u=,"-2"+t; ,(.h"-u-"+z)=o: f"=o. l'=o. [,=o. I 'F-u =, -2, (' 24 x" ax a: lx t. r-----i.:::fiepeBjpxa: r. = 0: Vl 0V0' 24 0 I ,=7,,81716 24=? 1; 6=6 rpaBrrlLgo. BiAno?iab: 7. +83. r) Jz' +l + "Gl =2Ja; zt+t+zJ@x+t11x-4+@-s)=4xl 2J2! - 5x - 3 = t + 2t 4(2x' - 5t - 3 = x2 + 4x + 4; 352 ill: AJfrEEPA Mep3rrK A. f. ra iH. AKaaeMiqHrai piBeHb ax,-2Or 12 x,-4x-4=Oi7x, 24l 16=OiD=1O24i xt=-!, r"=n. '4 repeBipxa:.r,=-;, V ;',r ir-B;=rV ; HeMacaMi.ry: ," = e; Js + ^11 = zJa; 4 = 4 - rpalsn6*o. BiAno6iA6:4, 4'[v 2', u$, a =,fs- *,', z z.[x + zxsx + 21. 31 7 = 8 - x: zu@ + r1s" + n = -t - 5r 4(3! + 13r + 14) = 1 + 1Or + 25r,i l2x' + 528 + 56 - 1 - l0x - 25e - Oi L31c, + 425 + 55 = 0t 13x, - 42r - 55 = Oi D = 4624.. x. = r, *.. = E. ' 13 lepeBipxa: r, = -r; '[ + G = '6; 3 = 3 - rpalrnE*o; bbFiEs6Es91672bt6_ '' : ' 13 113 ll 13 'lJ 13 Jra Jls JrB Jlt Jlg BiAnosiAb: -1. 4 "tE' 1-$r-=Jr-7; 5x-1 z.!1sr-tysx-4+u z=r-t; 7x 2 25!'-13x -2i 4gx, 28x r 4 = 4tt5r? - t}x 2): 4gx! 28x 4.6Ox,- 52x-8illJ, 24x 4=O: D=400; x. - 2,, r"=2.' 11 flepenipxa:,, = z; "E - "ll - "E; 1 = 1 - npaBsnLgo; 2EoTt2.r. ='_: .i--l-.i 2 .l--I -HeMa€3vicry.' 11 vl1 Vll vU BidnBidb:2. q 2,8 -1-J;-=E4: 2&' r=.r7a+lia. a@z li = t - g a 21p - 1gr + g + x 1i lzt - 4 - 2x + 10 = 2.rF - 19, + g. fi'+A=z,,lV -tor+s; 5r+a-.,f' 19**9; 25.r, + 30x+9=.r,- tox+ 9; 24t, + 4Ox =O:3"r) 5r_ 0;r,tlc rt, =0, I, IL3 fiepeBipKa: r . 0: 2J 1 JL = J-, - He Mac rMicry; *=-1, zJ-a ,[9=./-* -HeMaeiM,cry.3 !3 ! 3 BiA no6iA b : rlel.N.ae KopeEi3, 4a4,D Jt I>4i o,[3:r-I>0i.r>1.,- BiAnosiAb: (17; +*. 2l "G l<at OA3:r>1:x-lrt6ix. Bi1no1iAb: (1i 17. -------u .il:':.:itl! t::::::l::::l ::::5T':'.,q 1> 161 x> 17. 17 ' (rrq..l---: 1 17 q It I > -4; oc*irr,Iir KopiEE ap[ibMerr.:.rnr.ri, ro r , .ruc,ro, sfie Ba,qoBonbHse OAB,r€[1;+-). BiAnosi1b: 11; +-. 4 "!;- < 4, I{opeHiB EeMae. fr- ,'^ t-r 4a5.1 J2x-4 >Js --r: oA3r l:" I -* 1-'l're tz;sl. lr-.r>ui lrss: 2t 4>5-ri3x>9;x>3. tTrrrrt>)"i+RiOnosiAb: te (3,51. 2 A 5 ' ii*ltili{1i:l AITEEPA Mep3nrKA. r. ra iH. AKaaeMi,{Hr4i piBeflb l::t: 3Sg l2 yci rAE r0 s.,r. l
  • I*'0. [r+1>0; 5 -4 1,6 4 8 -4 BianoqiAb: ( -; 1) u [2j +-). qA6, D ' > J24- 'xr OIg: 24 - 51t 2 O, :( = 4,8i a) fltsLro ir - 0. 'ro r' 24 - 5.ri x t 5x - 24 O, /--=- '--- - ", = -8,; r" = S; r € (3; 4,81; -'----*-" : :t:noj on,.o i o. Hcllaa. po3B s3KiB. 8 0 3 4 8 BiAnoqidb: (3t 4,41. zt G<'6+r; oA3: ,r> 0; x < r + l; 0 < 1 - npaBlrnlHo. BiAnoeidb:te[O;+*- O Jx" +' < nlVi OA3:t'9+r>0; t(t+ 1)>0; ,.r=0; t,=-1; r € (--; 1l u [0; +*). t'+t<x'+1tl.<1. BiAnoqiAb: t E ( -; -11 ut0; 1). q nF a,*t , Jz' z; lr':-lr+t:0. ls*.6 lO-tr3: I ire I i+-' l2r 3:0: | 2 ) x' 3'+1>21 3;t2 5x+4>0t = 1; r,= 4: r e (4; +-- Bi.Anosiqb: (4: +-). sl .,6: r' > G, - ro; ls s" o- On3: I "r€( -i 41. L.r'-16>0i 8 'ic> t'1 - l6i x' + 5, - 24<ot Bi1noeiAb: |_8l 41. el J" z,*z.'ti"z,-tt lr': 3r+2>0. t ll on3:1,, x(l__;rlrrl2; -_). [2x'-3.r+1>0: 2] x' 3L + 2 <2r'- 3t + l; t'- I> Ot s).,,/i'+a'+:<z'+r; firrrro2x+1>o, "1,2 3r'+r-2 >0;r:,= 1; eionoaiao: I ?t + -) . it l a; .li '-' a . z' + z; ogz, :,. € [1; 6]. fiI{rro2r+ 3<0; r> 1,5; 7x r' 6<4r,+i2x+ 9; 5r,+ 5ir+15=0; *+x+3>0; r)+.r+3=0; D= 11; EeMa€ nopeHiB; r € ( -; +*), BpaxoByroq{ OAA r € [1; 6]. Bi0no6iAb: 11; 61. 4e7.1, J2 r>r.; O,[3:2 :]r>0irs1: a) rlrli{or>0,.to2 x>t2,xr+t 2<0: t:t = 2; jd2= 1; x e [0; 1). 6) nlirrro r. < 0, ro jr € (--; 0). Bi0no6iAb: ( *;1. 4 Jr.+7>x+1; OABir+7>Otx> 7i a) sftqo r+ 1> 0; r> 1, ro x + 7 >x2 + 2x+7i r'?+r-6s0; r,= 3;x"=2; re [ 1;2]. 6) sxqo r + 1 < O; r < -1; rel7) 1. -Bi1noqiAb: | 7;21. :t J*' r.x: O,[J:r ] -O:r., I:r =lrj' € (-*i -11 u [1; +-) | a) nlturo r > 0, ro a, - 1 > x,t 1> 0 Henpa Br'rnbrio, HeMae po3B'.{ariiB; 6).rxrqo jr < 0, ro r € (--; 11. BiAnMiAb: ( -t ll. q ulV-zr>s 4 oA3:.r, zrc > o: xtx - 2 > o: t = ot r=2t ,. € (--; 0l Lr [2; +*): a) nEtrro 4 ir > 0; r <,1, ro x'z - 2x>16 8! + x,; bc>16, I 2 f t I x> j: r)2-. raaoBoi6H'c on3r r. Lr;: .1 ]. 6) nnqo 4 jr < 0, r > 4, ro ir € (4; +-). sia,..ia,, lz?, * *). 13 ) sl ,[" ' 2,'; o,qB: J., + jr 2>o;r,= 2; ,- 2i x e ( -; -21 -r [1; +-): a) nnqo r > 0, to x, + x - 2 > !.t t - 2 > 0; r> 2; x> 2 aaAoBonllrse OA3. :ttii::{iiltiii ArrE6PA Mep3neK A. r. ra iH. AKaaeMi,rHran piBeHh lr::: 3S5 12" BiAnoeiAb: [ 1;0,u 9;1 . It OA3:r'+3r+3>0;r€fi. r'+3x+3<4r,+4r+1: 2 '3 l1 e - " :n[:7; o,(3: 1 J" > 0; rL = 1; ',.flrtrqo 3 - , > 0; t < 3; I 6jr+t:> 9(1 jc'?); 9 - 6r + ir'> I -gr'!: 10t' 6t > 0i (5r.'- 3t) o; J.(sr - 3)'0; =1; re[ 1;1]. 7! - :.' 6 >Ot x, - 7:t = 6 <O; ). = l: x,- 6; =N-=-Vttt1t '.'."""""'.'a:,i,1.tr.a..| l.:a i a.. --.... "i " """'4""'- '3 :..*..-.--Vz;-2 1x D J2t{+7 sr+2ion3:2r + 7 > 0; ir > -3,5: a) J]Ku{or+ 2>0tt> 2;%c+7<x'+4x+41 x2+2x 3>O.x,= 3:r,= 1ir€[1; +-). 6) sKrr{o , + 2 < 0, )c < 2, HopeEiB HeMa€. BiAno6iAb: 11; +*). 3) J3r r'<l-r; OA3: 3n t'> 0; r. = o; ir = 3; ,c e [0; 3]. .flllnlo 4 ,> 0; t<4, BpaxoByr.rt OA3, J'€ BianoqiAb: tO; 31. [0;3]. 354 aiit:AITEEPA Mep3ncKA. r. ra iH. AKaAeMi'{Hnr pieeuu :i:iji:i!il:.il:iiii'i:}
  • 6) sRqo r < 0, ror€ ( -; -21. BiAnosiAb: F*; 2l u (2; +-). 6) v/ ;'-;r. 5 ' 8 2.r: oA3: -I r 61 5:0; - F= ,-.---- - ,r' 6.r=5<0:.r, 5:.y, l:.rc t1; 5l: Y Y , a) r1.llro 8 2r ? b; r. : 4', .ro I 5 -t:z+6:.-5>64 32x + 4r,; -5t, + A8x 69>0, 5x? -38,r ' 69 0i .r.r. 4.6: x, 4i r E t}i 4j. 6) flHqo 8 2,r 0: "r 4. ro,r < (4; Sl. BiAnoqiAb: Gi 51. s 4. TPl,lrOHOMETPllgHt OyHKqti 1. BracrllBocri TpraroHoMerph,{Hrx OyHKqit 488. Pa4ianny Mipy Mo}t(na o6qHcnur?r ra oopMyJroro -.,. r! 25" 5n 180" 36 4) tr ' 1600 8rr. 180. I -. r 40" 2,r 180" 90 -. n-21O' 7ft 180. 6 4 2!3!: =72". 5)3.1800=5400; n.100" 5rr 180. = t; n.300" 5r 1ao. 3 3) 1qq = 20". 6) 2,5. 180" =.450.. 3) 6) 49o. 489, 3arrictr n cd,q niAcraBrrv 180.. t) ti8'= tt" 4) 1,2 . 180. = 216.; 497. 1) III .rBeprb; 2) I .rBeprb; 3) Iv 'rBeprb; 4) III qBeprb; 5) II .rBeprE; 6) I qBeprb; 7) 600" = 360" + 240", III qBeprbj 8) ?50" =360' 2 + 30", Iqseprb; 9) Iv 'rBeprE; 10) I .rBeprb; 11) 400" = 360' - 40'r-IV.rBeprE; 12, -470'- 360'- 110', III.rBepr6; 13) I .rBeprL; 14) III 'rBepr6; 15) II qBeprb; 16) II 'rBeprbi 17) -1,8t! = -5,652, I.rBeprb; La, 2,4n=7,536=6,28 + 1,265, I qBepr6; 19) 2,6r! = 8,164 = 6,28 + 1,884, II.rBeprb; II .rBeprb (90";180') ( 180'; 2?0") (1,57;3,14) III .rBeprE (180";270') ( 180"; -90") (3,14i 4,71) IY qreprr, (270";360") (-90'; 0") (4,71t6,28). 49-1. AoB}ri4Ea Ayrn nona o6qrcnro€rbcs sa OopMynoro I = Ro. t1 |.tz = a" 6*1; 2)2.12=24(c.M); 5n 12 3) "-= lon (cu)t 4l2fi t2 .24filc{t. 492, 1) I = Rctt I = 3. 5 = 15 (cM); 2 I=J19 =4,sn 1"*1. 3)Z=0,81!(cM). 493.r=3,14pa{. U!-t,rz; |rt,s; z)-t,52 >-z; -!;. 2, a1 r,Os r r; 1r 1' 4) 4,71 <4,8.+<4,8. 20) -4,25; II .rBeprb; 21) III qBeprb; 22) IV'rBeprb; 23) III qBeprE; 24 7 = 6,28 + O,72,I '<septs. 498. 1) II .rBeprb; 2) II qBeprb; 3) III .rBeprb; 4) UI s8eprb: 5) -380" = -360' - 20", IV trBeprr,i 6) 700" - 360'+ 340", IV qBeprB; ?) -800'= -720'- 80o, IY qleprbi .j.Iia:i:i:::j:iji: ATTEEPA MepsreKA. f. ra iH. AKa[eMi,{Hxi piBeHb ii:i 4s4. 1) o,7a5 -, rt X.t Z1 O,r. O,SZ; -, -! 357 IpaAycEa 10" 12 36. 80" 108" 105. 720. 824 240. PsAiaEBa Mipa ltyra n 18 n 15 ! 5 4n t 711 i 5n 7 4n 1,8rr 4n 356 Itl: AITEEPA Mep3rcKA. r. ra iH. AKaAeMi,{Hri pieerr :i:}j!{Lll{:i:}j.:-:l
  • 499. 1) (0; 1); 4) ( 1i 0); 7) (0; 1); 5OO. 1) (o; 1); 4) (-1; 0); 2) ( 1i 0); 5) (0; 1); 8) (1; 0). 2) (-1i 0)i 5) (0; 1); 3) (0; 1); 6) (-1;0); 3) (0; 1); 6) ( 1; 0). 8) II .rBeprb; 9) III .{Bepr6; 7n lO) - = -Ztt . lv vaePrb; 33 11) 5,5n - 4n + 1,5tr, IIe Eanencnr6 ,{oqEiil qBepri; I2l ij = 2n + -:. I qBeDrL; 6ti 13) I .IBepr6; 14) III qrepr6; 15) IV 'rBeprB. 5O7. 1t80": 2) 190'; 3) 45"; 4, 2800. 5OB- 1) 0= 90" + 36O"n, n e Zi 2) a= la0'+ 36O"n, ne Z; 3) o= 30" .360"n, n. Zi 4)a-135'+36O"n,neZ, 5O9. 1) o= 90" + 360"n, ne Zi 2) a= 60" + 36O.n, n e Z. 3) o= 135"+360"n,neZi sro.rr x q= ,l: , ]', 6=x. ],. -ir 6=0. ir3 x3 [r_3,0: lx 3=0. P-o3!'frrrcMo I piBHsdHs MeroAoM riA6opy: r: - r 6 = 0; a, = 2; r, = 3. po"r,"uu.", U piBHrHHe. orprMa.vo { = 3. BiAnoeiAb: 2. ?r-l _4 l0 9x. r3r-t{r i} 4r t0 9,(. x x-2 " -2x )t!.2t xx 2)' 3:t'-6x x+2 41 10 9:,r - ,k-4 =,@ 4: [a'' rr,+z=ro-s,, l'1, zy + o. PorB n)l{FMo I p BHenEq: 3n 2r - 8 0: , t00: x 2: r.. i. PoJB slr.Fvo Il p'B-AHHn: x , Oi x , Z. 6 BiAnoaila: !. 3 51'l " Hexan 40 - nirbllicr! MerIKaHqiB, rqo nporflrlarr 2 polir roMy. ,4^ = g8 200. o. ql , ,50.] : qa.,,o piBJnHH,, 88 200 4 I , , ,i;J , '8a 200 = Ao 1,1025jA0=A0000. Birro6tab.. 80 000 MernaHqiB. 512. 1) 2 cos 0o + 3 sin 90'= 2. 1 + 3 1= 5; 2) 4ts180' 2ctg90'=4.0 2 0=0; 9) 3) 4 5) +2= 3t 1+1-7 = -4: =r*1=r1,44 6) sin0"+tgn-sh4= 0+o (-1)=1j 5O1. Hexan I Ityr - 2jr paaiaE; II xvr 3, paaian; III Itvr - 5n paaiaE MaeMo piB- Etl',.t'. 2t + 3t + 5x = ni to, = u t= 2,10 '3nTHr -:: IT K)l .^: lllr{Yr'itu2 r3trrBtAnoaidb: : i -.5102 5O2. Heran I llyr - r pa,qialIl II ICvr - 3t paAiaH; III Rvr 4' pa'qiaE; IV l(vr - 7a paAiaE. CyMa BsyrpiruEix RvriB 'IorrpnryrErlra 27r pa{iaH' MaeMo piBHtHIIE: r + 3t + 4t = 7r = 2n; 15x = zn; x = 2]. 15 2n 2,t --. 8n "' l4t1 lKVr -r; IIHYr- -:tUKYr- 15 15 2n BidnaBidb: : l5 5o3. soBsiusili Kyr Mlroro&y?sq(a " +: = +. cvMa 3ocsi nix RvriB' v3'rIrx 15 15 ro oAsoMy trpr l|oniEin Bepu' i - 2r. n=2n: *4=15 ' n= 15' 15 Bianoeiab:15. 'r 36 n 504. KyTnpuorHoBi prBBo6erpPHororovts)rHYKa{180'-36"r:2=72':3ti" ,16"- 5: 2n 5 3irJ 11ir + 2 10 9r. x1x 4 = 1(r 4t 2T 8n l4n 5' 15' 15 2n 2fi l; 1; sin,15o + cos45.= ta + fa = Jt: sn.6o.+.os30 ,:i ,:)'=l i=l ,,, sin45"cos45'crsso. = * ; n = *, 3tr tcosn + 4cos + 2cos2,r = -5 + 0 6sin.1 zcosl + tgI -7cts!=g z"r",l *".",1 = :.1 4l' -l €l'4 6 .2) 2l 5O5. 1) 90" ra 270'; 3) 270" ra -90'; 2) 180" ra -r80'; 4) 360' ra -360". 7) 8) 506. 1) 400'= 360'+ 40"; -320'= -360" + 40'; 680" = 360' 2 + 40'i -1040'=-360'3+40'; 2) 510" = 360" + 15O'; 870'= 360" 2 + 150"; 1230'= 360' 3 + 150'; -210'=-360'+150' 358 i::i:aITEEPA Mep3nr( a. f. ra iH. AKaaeMi'{Hui piEeHb :::::::::::::::::::::::::::: iii::i::.::'ii!::ii AnrEEpA Mep3nc(A. f. ra iH. AKaseMieHhi piBeflb ii:l 359
  • 6 "t'( , (^ E=: 514. ror shrts, n","n =@.1-.] l'.ut. l=1..'' ---'3'- 6-'6 2 lJ3.l 2a 2 513. 1) sin 270'- 3 cos 180" = -l + 3 = 2; 21 "."6s" * "i,'3s" = 1* 1= 1,' 22 3 7 te2 45" - 3 cts 45' = 7 - 3 = 4) 4) sin 180'cos 120" tg 60" = 0 cos 120'tg 60'= 0; "tnl+cosn+ts] I t+1 -bl- 2sin1 2 ! 62 6) 7') 8) 1) Il=.:nn.@.o.rr, zsin 1= z l=t; sin 2d. 2 sinoi 6) 3 2 6 2 - "t;'11 - "*" =0: Scosj' - "v": cosBc' 3 cosc. 6t 2 6 2 2 515. li 1) sin4.n sinn=0; qsinft 'n 9=zJzr sin4P' 4sinp''442 2 qq L= rgr o; 41gI=4.t 4i ts4pr 4isp.'' 4 ' '4 516. O6nacrE sra.reEr, y = sin r: y e [-1; 11. O6"racrr, axavenr y = cos t: y € [-1; 11. O6nec1l 3Ea.relr, y = tg rr y € (--; +-). O6.racrs sEaqelrl, Y = ctg t: Y € ( -; +-). 1) ; €t-1i U, pisuicrl, MoxnrBa; ./is z) -4- = -u'9/. prBEicrb HeMoxr'lqBai 3) -V1J = -1,06, piBgicr" EeMoilc,::lBa; 4l 1= 1.05. Dilnicrr, HeMonrnrBai 3 - 1t -_-_5l - = u. /60, prBErcrl MoxJrtrBai ot 9-rl. DiBEicri, Heaaoxnr.rBa: 88 7) piBnic$ MofinlrBa; 8) piBnicrb Moxn sa. 360 ll.::iAJTTEEPA Mep3rqKA. r. ra iB. AKaaeMieHxr piBet" ll.t*l:jtii:liii:i . 'r " .-" JE 'E Js zJs ,E. srn4 cos-.crs3 Z Z Z=t.l t, *"1 "t"! r.tc!= o+1+o= 1; 6cos0+4.sin2r' 4sin'? 2ai =6+0. n lf]' =u- f.' n lac 517. OcKinbns Y3 = 1.t2, ro 3flaqoHsa sin Ct, cos o }re Moxyrr qopissrcearl,l !.1 2 " '-.'----- "' z', 3IIaqeE .s tg (,, ctg c! - MoJrtyrs. 518. 1) -1 < sin a < l; -3 s 3 sin c{ < 3; Hai6i{bme - 3; HafiM€nIIIe - (-B); 2) -1 <cosd<1;3<4+cosc[s5;Han6inbue-b; IIsriMeIIme _ B; 3) -1 <sincr< l; -1 <-sin&<1t1<2-sind<g;Eai6inErEe_B; HaftMeII- rre - lj 4) 6- 2cos s; -1< cos d < 1; -2s6 2 coso<8; Hai6inbrre -8; 'IaiiMeEi[e _ 4; 5) 0 < sin'zs < 1; Hari6irEue - 1; IrajtMeEltre - O; 6) 0 s cos", o< 1; 0< 2 cos,o< 2; 3<2 cos, a < -1; Hai6inEllle - (-1); EaiiMeI{- llle-( 3). 519. 1)-1 scos q< 1; -5 < 5 cos([< 5; Haii6inbue - b; EanMeII e- (-S); 2) cogo - 2i 1< cos a < 1; -3 < cos a - 1s -1; sai6inbme (-1); IIanMeE- Ille - (-3); 3) 0<sin'2d<1;5<5 +sin,d<6; Eaii6irbrre - 6; EafiMeHr[e b; 4) -1 <sir d< l; -3< 3 sin a<3;4< ? - 3 sina< 10; lafi6i,rbure _ 4; sai_ MeH'tr€ - 10. 52o. l, sin.r = r: r. T: '- =n , zn - 5n ' gtr . z Z ,7, xxl --4ft= 2i 2) sinx= li *,=-I. *" .-n+2n 3n n 7n . 2 2i xs=-2 4=-. 521. 1) cos .r = 1; xt - 0; tz = 2ni ri = 4n 2) cos r = -1; ,r=nix2=n+2T=3n;as=tr+4n=5n. 522. 1' iinz.I + "o"2 4 44 srn +cos 1+0 1 2 sin a + 3.1 1+r 1r 1222",nfr-11*,r,34 12) '4 . /n n) Brr ,, "'"1 3'ul sin 6 =_L=o./n nl /r n 3n Isrnl +cos , aln -+cos +1, 36r!36i662 ^. I 1 n" I n n"3) i st' ; + "," ;J -|."'" ; -"'';,l = "r., f , z"r' [":" f -"". I -"',, fi = =2"i"[.i'i-"i",' =a"r'["r'i = ^ i,: "E Va.n[J-11 ,"0*"1 J-.n^] ,6"rnn.,Jzcosr 9rr ^-523. t ) ,ni 5n ol"rnln nl rnn",'n I JB J3 "12 6/ -3 6) -4 -6 = t'rtu '*, t; _ "r"; ; !5 _1-+_, JE cosr - Bsin4 1+ 3 4 2 2) ./^n) r fl 6,/ 6 -3 -"(t ll ,.,"1 r.1* r.lJ 3) ! 3 6) iliJitilitliii AITEEPA Mep3nrK A. r. ra iH. AKaaeMiqHur piBeHb ,!j:: 36i
  • 524. 1) sin x = li x = - + znn, n e Li 2r sin r t: .r ft -znr, n -Z-'2 525. 1) cos I = 1; t = 2nn, n e Z; 2) cosr.= 1; x=n + 2nn, n e Z. 526.9 tgr.r D(lg'): x ' - rn.nr/i A = cLg kt D(cl'g tt t t n + n' n eZ' BiAnosiAb: se tcEye. 527 . 1) cos x. = a + 3: -1 < a + 3 < It 4<a< liael4. 2l.. 2) sin n = a' + a; a' = 0; rt = 0; 3)cosr=d'-1, 1<a' 1<i " ' t. ], =2. [" ' -,t2, J2.. ", I Jz,,El, Lr' t: 1r a'>oi Llle,Q: 4) sin jr=a' a-1;1<a' a-7<1; fo' a-s l. , ,'-----,--; a ot_,, .jppir; fa' a -z<o. la'-o>o; a € [-1; 0] u [1;2]; 5) cos n = d'? - 5a + 1 < a' - 5a = 5 31: a sa+5: t, I;- 5a-4 '0. o _ lrr 2l! l3r 4l: Ld'? 5d+5i-1; ld'-54+620: at26 lFt - i a+2." 02 1 531.1) y=Z_"i.,, l' srnr:l; I s2 sinx'3: 1. 1 . r, ,,.11, rl, 3 2+sin,r - L3 l Z y=: 7 : I .osr l:-1 :-cos,r. tlO. I cos.r:2;" 1-cosr I I [] -t <+-.r€ -:+-l-2 l-cosx ' 2 ) 9 532. l)y !;:-;: -laroEx' li I / .cos.r:1:2:3 cosri4: l 1 1 I 2 11 I- -!_t < aL rLt_:tt: 4 3 cosr 2 2 3-eosx " L2 ) 2J g I ., -1 :sin,rl liO<srnr 112; 1 1 lr ) 2- s;n,1--i a'l2t - ). 524. 1)sint=a 2i-1<a 2<!; 2) cos r = a' + 2; ocllinEnrl a'9> 0; 3) cosr=a'-3; 1<a' 3<1; a'-3<1. fo' +so. lo' e--t, lo'-z-0, ".1-z; "E)ul"E;z); 1<a<3; a€ [1; 3]; d:-2 0, ro l asxx rHaqeqb r JJe irH) c: 533. npu noBopori OC,AD, EaBKo,ro roqna O na &yr - nporrr roanr {nroBor crplnril, Bln IIe- peiiAe B.npnMol(yrHl{n OC,BD,, to(i OD2= ODt oc,= oct, cosl -a t" OD OD, = -q. = -sino;2 sin s =.-(-sin (:r); sin c[ = sin d. ,qoBeAeHo. 534. npl, troBopori OClAD1 HaBKono roqrtlr O Ea K!-r'rr trpo1h ronhHHrr{oBoi crpirxx BiH nepefiac B npfl- . Monyrrrr& OC,BD,, ,roni OC,- OCJ OD,= 04. cos(n + rr) = ts = -OC, = :OCt- t^= cos 6., cos d = ( cos c{); cos c[ = cos o. AoBeAeEo. 535. 1) -A(r; y) e I qBepri; jr > 0; y > 0; 2) A(ti y) e II qBepri; r < 0; y > 0; 3, A(x: V) E III .rBepri; n < 0; a < 0i 4) A(x) vte IV.rBep"i; r>0; u <0. 4 si,n rc=2a a'=2i 1<2a a' - 2 < 1; '1 < a2 - 2a + 2 < 1; o" 2a-2't. lo 2a t 0. ra lr'z' 0. !'=t' , ,. o'-za.r.-r )a . 2atBzo: la - 2,r3-0: o'R: 529- OcIlirLRr 2 sin ct - sin'd = sin(2 sin cr); sin ct > 0; (2 sin c[) > 0' ro 2 sin rr sin'a . 0i 2 sir c' sin: o. 53O. SEaiiAeMo ssaK pi3El-rqi cos 10" - cos 10' cos 20'= cos 10'(1 - cos 20')' cos 10" > 0; (1 - cos 20") > b, ot*"' cos 10' cos 10" cos 20' > 0; co.s 10" > cos 10' cos 20'. ra iH. AKaAeMiqHl4i pieeru :;:;1!::::;i:i:i:i::i;i:i 536. ll/lx) 2h-_ ri Un: x--5:r.=5- flrvprp qHa eraHocuo roqR}i O: I xt3 " t' " , r1;= 2-t : r'nannar z) f(4= lx": ,(Dr R; crMerpu.rHa BiaEocHo roqlrr o; r( r) = iF l' = -i,F, lenapra; sl f @) - dV; ,(Di -a; crMerplrqtra Biagocgo rorrxr.r o; r(,)=i/Gt=tr?, rap'a; a, f@ = 2r7 + 4x5 - 3'; ,(D: R; ctrMe"p@Fa Biasocno roqr$r o; f( x)=2(-x1 +4( ')5 3( r)= 2t7 - 4x5 + 3r = -(2x1 +4'5 3r), EenapHa; i::iiiitiiiii{i: AITEEPA Mep3neK A. r. ra iH. AxaaeMiqHnfi piBeHb i::i: 063
  • 5) ft,rt = -;l-; DU): .t t 0t x z 2i x = 2. cl{MerpL{'IHa BiAHocHo rot{Rlr Oi Y' - 4v' 55l(- t - .-i, napFa; '' t-xl'-4(-x)' x -ax' o) /(r) = i/rl; D(r: li; cxMerpr.rHa BiaEocEo ro'{ti' o; fr xr=t4l fi. *0''". 2. 3HaKr4 3HaqeHbrp1,lroHoMerprl'{H1'!xOyHKLlii s42. 1) sin( s0) - 2 ts(-4b.) + cos( +st = -f,+ z.r+$ = ri.* =t.{, a stso + zsrn[-r) - r"*[-;) -.-"f-;) = s. o -2. 1 + a. r + r. o = z; .,( n ./ nlLb+srn'l--l-cos-l I I 6/ 6l ,.r.lrl'-l@1"2) 2) r,5+0,25-0,75 2."tE 2 rJi Jz2 543.1) ssin(-45') + cos( 45")+2sin( 30".) + 6cos(-60") = **9-r.!ru l= 2222 - uE tz=2-Ji: ""'" '"Ei 3 s 6 ,-2, sjn'z(-60.) + cos'z(-SO") = Yl +L 2) 2 rt zt"J ll.,*1 -o1 rssinl-Il-q"osf 1l=z r-rr (-Js) Fs.r-r)+4.Jq=-t 4t -t 6) 2) i6i --'-'-' 2 =zn6-a+zJ5=d5-a. 544. 1) sin100' > 0; sin132' > 0; sin100.. sin132" > 0; 2) cos210" < 0; sin115" > 0; cos210'sin115. < 0; 3) cos285" > 0; cos(-31q') = cos316o > 0; cos285..cos(-316.) > 0; 4) te112'< 0i sin165">0; tg112..sir165"<0; 5) cos318'> 0; ig(-214") < 0; cos318"tg( 214") < 0; 6) ctg300'< 0; sin220"<0; ctg300'.sin220. > 0; 7) sinl>0! cos2<0; sinlcos2<0: 8) sinS<0; tgs<0; sin5tg5>0; 9) sinS>0; cos4<0; tg5<0; sinScosStgs>0; 10) sin(-118)<O; cos118'<0; tg118"<0; sin(-118")cos118" tg1la" < 0. 545. 1) sin102" > 0; cos350'> 0; sin102.cos350" > 0; 2) sin134" > 0i cos131" < 0; sin134.cos131" < 0; a) sin lsz" > 0i cos256.<0: "ll-.]jl. s, cos 256" 4l cosl42'< 0; "inzz" O; "1"1=?. O; sin?2" 5) sin112'> 0; cos(-128') < 0; tg198. > 0; sin112.cos(-128.)ts198. < 0; 6) sin( 245) > 0; tg183" > 0; ctg(-190") > 0; sin(-245) tg 183" ctg(-190.) > O, s46. Ilsino!gc- 0i zt "in'-9.0, 3.1 "in'o.0,cosd cosd 4) sin s - cos o > 0, ocRinL&Ir sin c{ > 0i cos d > 0i - cos a > 0; sin o + l-cos d) > 0. [r:tlliltilll{i AITEEPA Mep3rcKA. r. ra iH. AKaaeMiqHni pieexs iill gos sxs(-i) "t"(-;). 2""<'r. n"''(-;J ='6 G * z. ca * a (@ =3 2+4.::=4i 537. 1) 38" € I cBepri; 2) 119" € II 'rBepri; 3) 196' € III'rBepri; 4) 302' € IV qBepri; 5) 217'€ III .rBepri; 6) -74' € IV csepri; ?) -98' € III 'rBepri; 8) -285"€ I.IBePri; 2n 9) -- € lqBepfli tor 91 e rI qneori; 5 7,t lll - F tll qBeDTr: t:r !! e Iv qseorir '4 rrt -4 e lll onepri: l4r !I e r qseDril 4 16n 15) - o e lqBeprr. 539. 1) sin 186' < 0; 2) ts 104' < 0; 3) €os 220' < 0; 4) cts 340" < 0; 5) sin( 36") < 0; 6) cos( 78') > 0; 7) ts( 100') > 0; 8) cte( 2s1') > 0; I 54O, l) sin(-30') = -sin30" = -!; 2) te(-60") - -tg6o" = -!5i 534. 1) sin 110' > 0; 2) cos 200" < 0; 3) tg 160' < 0; 4 ctg 22o' > 0: 5) sin (-280') > 0; 6) cos 340" > 0; 7) ts (-75') < 0; 8) cts (-230") < 0; 9) sin (-130') < 0; 10) cos2<0; 11) sin (-3) > 0; 12 cte L,7 < O; 13) tg 1> 0; 7ft 14) ctgt < ui 1n toa<o:' "6 2n 16) cos S <U. 4', ,.."(-:) 9) sina > 0: 7 ror tE9I > o: "a / r 3nr 11) cosl- 12 J < u: / r e"lt2 .to _-t>u.' " 12) 3) ctg(-45') = -ctg 45' = -1; 6 a) cos{ 3Ol = -cos3o" = ;. 541.1) cosl-60"t- re(-45"1 .os60" tg45"= t, ,=-fr, 2r ctg(-60)sin(-45")cos(-4s'l cts60"sin45'.os45"={ 9 + f 964 !1{: ATTEEPA Mep3rlrKA. r. ra iH. aKaaeMiqHnl pieexu ill:l:i{;}ii:i!i;i I I M Jz
  • f sinB 547. ll sin P cos P 0: 2) " ,'0 r 0: 4) sin 0 - cos 0 0. ocKiibK sin 0 0: .os p 0. ,1 lEl . o' srn li 54a. 1) te 130'< 0; ts( 130") > 0; ig 130' < tg ( 130"); 2) tq 110'< 0; tg 193'> 0; tg 110'< tg 193"i 3) cos 80" > 0i sin 330'< 0; cos 80" > sin 330"; ar 8n 4l sjn 60" 0: sin -" ' 0: srn 60' , .in i: ud ,n 5) .le 1' 0: .os 280" 0: .te:' cos280': :l tJ 6) ctg 6 < 0; cte 6" > 0; ctg 6 < ctg 6". 549. 1) sin 200' < 0; sin ( 25o'.) > 0; sin 200" < sin ( 250"); 2) cig 100'< 0; ctg 80" > 0; ctg 100" < ctg 80'; 3) cos 250" < 0; cos 290'> o; cos 250" < cos 290'; 4) cos 6,2 > 0; sin 5 < 0; cos 6,2 > sin 5. 55O,1)sino<0; sino sin(r =si c[+sin(r=2sino; 2) cos q < 0; cos c, cos & = -2 cos d; 3)tgc[>0;tgCr-tgq=0. 551. 1) sin B < 0; sin P + sin I = 0; 2)cosP>0; cos0 cosB=0; 3) cte li < 0i -ctg B ctg B = 2 ctg 9. 552. l) sin o 0: cos c 0: o . ll qBcpli: 2, sin d , 0: tg o 0: a L TTT qBFPri: 3) sine=sin.r; d € I qsepri a6o a e II qsepri; 4) ctg cr + lctg la = 0; (1 € II qsepri a6o ct € IV'{Bepri. 553. 1)coss>0;tgcl>0; d€ I'rBepri; 2, sin a 0: ctg L/ 0i c, - IV qBepri: 3) Lcos nl = cos cr; o € II .IBepri a6o (r € III 'rBepri; 4) ltg c4 ig d = 0; c, € I .rBepri a6o o € III'iBepri. 554. l) /(x) = sin'? r Dltt Rt ll r.) sin'{-rl sin ir' napHa. Le{ -x) Ls r T lv)=:b-. Dl)t x . Ot /{ x) =:- --. r,aptsa. 3) l(is) = tg ' + cos x) D(f)t x +71h, k e Zt f( r=tCCt) + cos (-ir) = = -tg r + cos rc = (te ir - cos a). <f'yHllqin saranbHoro BltrrsAy. 4r /rxr-f "o"'. otn, I cos"r' 0; xtn-2nn,n'Z: I +.os r I - cos( x) 1- cosir /l -rl -. naDlta, ' 1+ cos( x) 1+ cosr 5) l(i') = '3 + cos jr; ,(t: Il; l( ') = (-'f + cos ( ') = -ri + cos 'rr. ovl{xqis 3a- ranBEoro Blrrns,ay. ir sin.r 6r /rxl= ^ : D{/): I cosr'0; cos,r- Ir'r /nh.hcZl 1 cosr .rsin(-r) x sin,r ll-x)=-= - . napHa' I cos(-xl I .osx rr /rrr . (r - 1) ciii D(/): x - 1. ovHrq' Jaran6Horo Br.1c*av r-1 8) /(xr= r sinr: Dtni',oi 1-'1 {-:rt s'nr x1 n:11I. "enapHa 366 lli anrEEPA Mep3neKA. r- ra iH. AKaAeMi'{H}ri pigeHb {itliiltii:ii:!:i: 555. lf /rr, = tg .r - .Lg xi Dlf:.(?nk,*c Z; x t+nn,ne/; It xt tg.r - ctg n ttg -v ctg r1. n.nrp"u. 2 2) /tr) "in"*r8'. Dtht x , : . nh- h t- zi .in , tgt=0; srnx tgx 2 - sin,r - sinxrcosjr 1r lsinx*O. lx, nn.n-7.stnr-- ?u. _ /u. I "_^ :::: "_, cosl l'o'r ' r': lr '| znm'm' Li " 2 -'" - - ., -. s,n( "r)- te(--r) (sin/+Ls.r) sinr r{sJ. -*rr,r.z /' ' ' = sjn(-r) - ie(-r) = Gi" r - ie ") = si", - tg r ' "ap"s' cos( r)3) /(f,) = :.''' : Dtn: !. !7i /'-x) ("-;t = "i*, . nao,,,. tt 1,n= t!''r, Dtni x-li , , | ^*.r-2, DO se cllM€rplrqHa liAEocHo roqrll{ O; ibysRr{in 3arar6Horo s}rlnsAv. 5.1 l1r)=cos;r+f; ,(r:.R; l( r) = cos(-'l * i = "o" " * l, u f@ =*#+a; D(n: r+ tt; ' + nn, n e z: .. clgt r) l-x )2 1) crs). (.r' - l) . HenapHa. (-.!)'-1 x'-1 556. 1) G' 36=VtJrL; x, 36=2x- t;f ,2r Bb=O:11= .Et',=7, IlepeBiprca: ', = 5; vE6-36 =J 10 1; ./:rt=J tr; aeMa€ sMicry; n,= ?; "4t- 36 = vt4 r, fis = "{3.Bi)no7iAb: 7. 4 85-3' r=r; '[r-ar=r+rt rb- Bx=:t, +2r + Lt f + Ex 14=o: x, = -7; x2= 2. lepeBipxa: r,= z; -1Es+zt-t--7; 5=-7 - seirpaBu,,IEso; r, = 2; - u/t51-1=z; 2=2 --EpaBo,nbEo. BiAno?tAb:2. UUr.rrr' 3! s, .( -2x 3(x h. - Jr^ 6,r,6 ' -5rr6 x B xt2 t)i r 2-'oi r,2 =o: lx' 5r r 6 = 0. l.r I a6o.r. = 6. -->Z-- Z--,'- [r-2=0: ltr z. -2 I 6 BiAno?iAb: C*: -2)u[ 1;6]. -. r'?+3x- ^ x'?+3x+2(r 3)- ^ r-3 r 3 J{ ,5r.-6.0. I,r --baoox, ,.--=-y-}---V- . l,-s+o; ir+s. -6 i i a BiAn@iAb: [.6t 1l u (3; +*). l'=-t' 3)rjf 1xr.- 2)x. 3) 0i(.{-1)(.r 2111 31^,0; l;r,2, -i/-='a-V .r 3. -3tt BiAnoqiAb: e*: 3) u ( 3; -1) u (2; +-). :tlliiitiitlii:l AnTEEPA Mep3neK A. r. ra iH. AKa,qeMi,rHran pieenr flir x'?+5r 6 - .r:+5x 6 l a:u: , 3 =0; 367
  • 4) (r + 2)(x - 1Xr 3)'< 0i (' + 1Xx - lxt 3)'= 0; --Fr-=,,'T,'+ -2 13 BiAtuosi)b: l-2', rY, 3). l-fi rypncr 28 2a 4 2-rf, r!?ncr ! 2A 28 c 4g 4 IIepEe piBHsnHs: 2a247 ; i-6 ,4pyre piBHnrrtrE: 4x+4V=56 560. 1) sin4m" = sin(S60" + 60') = sineO'= @; l, = -2, l-=' L'= 3. 12' 13) 14) 15) -. 23r. - (., n . t rl n "Es,n 4 -srnlon-4J s'nl--] =-srn4 =--: ","4="'"[r" ]l ="i".-^l . -.r"r--. 6, 3 ! a) -" 3) -"'3 2' 7n /- r) ( n J2. cos-=cost zr =.os _ t= :, 4 t 3) 4) 2 /19'11 l9r / ntcL -3 | tc a = - tcltt'r ' 5J = - tc; v3. 558. {28 28 7 MaeMo ctrcreMy: l;-i 6' I4x+4a=56t 4 4 I 24/14 xl-24x 14x + x'1 Po3B'sxieMo lpyre pil""""", j 1a_,:-i=or -"'" a;at'l;i-" " =0; -r2 - 62x r 436 _ n. lr' - e2r . 336 = 0, I*, - 56 a6o r, = 6, s6 Ee 3a.qoBorbHrc 6x(14 -.jr) l6x{14 - x) * 0; lr. , 0, .r * 14: . l.r = oi !'MOay 38,qarrl; I -lu=6' Bidno6idb: 6lrM/roA.; 8 EM/roA 3. nepioAnqHi OyHKrtii 559.1) sin390" = sin(360'+ 30) = sin 30 = l; 2) cos420'= cos(360'+ 60') = cos60" = l: 2' s) ts 780' = tg(360'.2 + 60') = ts60" = J'i 4) ctg 405' = cte(360 + 45, = cteL,d = 1i E 5l cos{-?50") - cos750'= cosl360" 3 ' 39'1 sG36" = f, r 6) sin( 390") = -sin(360 + 30) = -sinso" = -l;2 7) !e( 2lo') = - te(I80'+ 30') = te30'= -*l3 8) ctg225'= ctg(180" + 45o) = cte45o = 1; s, cos300' cos{360" - 60") . cos(-60') -"oo'= j, l0) tsl50"tc(180'- 30")= ts(-30') f ' lln r- rr / nl t vb 1l) cosj-=cosl zn-= =cos ^ =cos-= ^ i b o./ o/ 368 llt AnTEEPA Mep3rrKa. r. ra iH. AKaaeMi'rtrlri piBeHb iijtit:lil::titi:i t; cos4050 = coa(360'+ 45o, = cos45" = l:: 2 tg( 325") = -tg315" = ts(180'.2-45)=-tg(-45")=1; 1 sin I I l0' =sin{360' 3. 30")=sin30.. ;i te?65" tg(180" 4 + 45') is45" = l; 7r (- n E Icos-=cosfzr+t] = cos- =,i 5r! / nl cre4=ctcl'r r 4J = cts:= l: .l 9,r' In fit rr "E4 . -srnlz'r + 4) siLn 4= - '; I 2) 3) 4J 5) 6) 7 8) n, ""[ 'Sl=-",*'!*- .,u(r"-;J ",";=-f s61. a) I iiltltiiliil{t{r earesPA Mep3nrK A. r. ra iH. A(aaeMi.rHrn pieenu lld gOg
  • T 569. Hexan Mixc ABoMa cenaMn r l{M, roAi lenocrreAucr Aorae qro Bi{craE} sa a rpaRrop * -a *o. Benocsnearcry trorpi6Eo sa 1 roAr{ny 6irBue. r 5r-3r 60 rvracMo prBHssHq: ti. 6=1, 60 . -: 2x 60: r 30. BianBiAb: 30 kM. 4. BracrlBocri i rpaoiK]a OyHKqit y = sin x i y= cos x szo.rl af-l;-rl; r=-"f-*l' r=o serpaBrr.rl'o, roqriaA H€ Ha,',e)(,rrr, t 2 ) 2) rpa4ix]: ". -lsn. ,E uz s* ,E ., i .'"2t Bt-t 2.i 2 cos4:; *.l." ;j, ', ', , -"., B Ha-1F){,r6 rpa0lry; 3C( Lnr 1): 1=cos(-4n); 1=cos4r!;-1 =1 HenpaBrnbFo, roqfta C Ee Ha,,re ,{rrrL rpaabi$y; 12 563. flItqo f(r + '1:) = f(x T) = f(x, ro " - repio,q OyH$qii l(r). rr rrrr cosx: /r'.rr .o."'9I="o.lrn 'n)="o"'. Aou.q"no. 4 " 4 4) 4 2) f(r) = te lxi ( 2n /{r. + It tg3|x - ---: ] - Iel3.y 2n) = Lsl2r 3,rl = - ts{ 3x tg3x. AoBFAcHo- 3) l(r.) = cte 'rir; f(r + T = cts n(' + 3) = cte(nr + 37t) = ctg n'. AoBeaeHo' 4) fi.rl = sint5r 2r: (t /lx-r) sin s r-ll zl sin(5ir-2r4,rl sin6.r 21. AoBFAcFo. ,t l s64. lr /r.rr cos 3.r: /{x ., n .".3[" - ?) cos{3ir + 2r) - cos3ir' AoBeaeHo. 2) l(jr + ") = cos 3(n air) = cos(3r - t2n, = cos(I2n sr) = cos-3.i. Aose,qeso. 565. l(:r) =sin r; l(j' + ")= sin(t + n)= sin r.; r IIe e 'epioaoM abvtlllqii. 566. l(r) = ts jr; / nr (n ) [t.t . rt = tE,! )) ,t,i r, .,s*, - I He . ucpioaov SvHRuii 567. 1) l(r) = r'? + 2; rpaoilc napa6o;ra, <eirxur EarpsMne{i Bropv, r.oopalrlrarr BeprrnEr (o: 2; f(r) e [2i +*); 2 f(x) = rz + 2a='2 + 2x+1 1=(' + 1)'? 1; rpaoin rapa6ona' lBirRIfu nanpsMneHi Bropy, xoopar.rHarrr BeplrI{IIlI - (-l; 1); l(r) € [ 1; +-); 31 11;i=2./r+3; < BirRa, lapa6onr, BeptU'Ea Mae ICoopaI'IHar' (o; 3); l(') € [3; +-); , 4 f(r) = 4 3G; <sirna' rapa6on', Bepn'FIa Mae rcoop,lurlarr (0; 4); l(,r) € ( -; 41. 568. r) "6.* V7 VF v? {z "F z, ,) 1616 Vt - 'S' a V* = 'VF lF = .'F VF = s, ",:14=e-rc2=:trt =g=,' VsJt 'i's" 2 {2'' V2' 37O i::t: AIfEEPA Mep3ncKA. f. ra iH. AKaaeMi,{Htn pieeHs iii:ilil:ilii::::i roqlla B Ee Hane}rlrr6 rpaoiKv; -[ltn 11 1 n] 1 r r I D B :dt =cosl4r--]: =cosBt ,=r; ro.rfta, sane?I{I,rb rpaoiRy. ,rr.,, o( l, r'1, -r "r"l ll, r=.r:roq,.aA Hanc,,*nrb rpa{i*):t 2 ) , 2) /n 1 1 tr 1 2 Bl-: : =sin : -=12 21 2 2 2 3) C(nj 1); -1 = sin n; 1 = 0 n, ,l?!s, _ lJ, -1= ","?pa,I 6 2) 2 6 rpaOiKy, 572-1) 3n -2n: -n:.0,2n:6n;7n syni OyHkqii; 2) Han6in6moro sEaqe'na'$yurcqir Fra6yaae "r" -+, ;, +, 3) EanMeH'roro 3Haq6EHn oyEriqis Ea6yBa€ *" Tt -;, +. 573. 1r Hvni dvHk'ii: 5n: qI. r ' 3n. 5n. 7n. 2' 2 2' 2 2 2 2) san6inBuoro sHaqenH.s OynRqin Ha6Fae trpn 0; 8n; 3) EanMeHrroro 3HaqenHs Oylr&qis Ea6yBae npr r; r; 5n. 574. y = sin r € opocralo.rorc IIa trpoMiflr&ax l); 4). 575. y = 5in , " "o*t orc sa npoMiniEax 1); 4). 576. y = s6s 1 sra{.. Ha rpoMiBrcax 2); 4). 577. y = cos r 3pocra€ Ha rpoMirriKax 1); 4). 578. rr cos t.6rT .os r.68,r. o.tsinbHH Ha ]'1,r"l 6u"*o'" "o**., 2) sin 20" < sin 2l', ocEir6(s Ha [0; 90'] y = si1r rr..r... 3) cos 20 > cos 21", ocdrbtiu Ha [0; 90"] y = c6s r..rr^... :::l::all::il::ri:! AIIEEPA Mep3neK A. f. ra iH. A(aAeMi.rHri piBeHb ::it 371 HenpaBrrnbHo, Toqlra C Ee da,re)r ,rrB rpaoixy; 1(nrr-t = srn[4n 6), ,= - 2, ro'rKa r] Haie].'rrL
  • l0't 25r I 3nI 4) s,nl- > srn 18 , oc}(r,lbr{H Ha lfii.2 I y = srn .r cnaaac; tor 25n I 3nl 5) cos-9 <cos t8, ocxrnbxn f,a itr: 2 I y = cos r 3pocrac; 6) cos 5,1 > cos 5, ocKinExn Ea [4,71;6,28] y = c6s 130o"t""' 7) sin 2 > sin 2,1, ocKinbxr Ea [1,57; 3,14] y = sin t cra{ee. n 4n lnl 579. 1) cos;>coE;:, ocftinbl(r Ha l 0r ; l y = cos r cna,qa€; 5r! 1711 ln I z) sin I >$n Id-, ocxl.nbKH 3a Ltitrl y=s)nrcna4ae: ( zft l' an) 7n 3'l rr) s,nl so.J >s'n[-loj: -$n30 > srn16, oct(r4hlcn as Y=sintspocra€; lon l1n i 3nl 4) cos Z->cos t, ocEtnbKr Ha I tr; 2 I ,, = cos t 3pocra€. 580, 1) Ha npoMirrc&y ll,57i 4,711y = sin .' cnaAse; sin 4; sin 3,6; sin 3,2; sin 2,4i 3in 1,8; 2) sa npoMirGy [3,14; 6,28] y = cos t spocrae; cos 3,5; cos 4,2; cos 4,8j cos 5,6; co3 6,1. 581. 1) Ha rpoMbracy I-1,57:' 1,571 a = sin x 3pocrae; sin 1,5; sin 1: sin 0,9; sir 0'2; sin (-0,2); 2) Ea IIpor.blCICy [o; 3,14] y = c6u " "o*""' "os 0,1; cos 1,4; cos 1,8i cos 2,4; co8 3,1. 582. 1) sin l23o sin 132' > 0, Ha npoMir{rRy [90'; 180"] y = sin 'r cna4a.i 2) cos 4,2 - cos 3,4 > 0' Ea rpoMitrKy [3,14; 4,?11 y = cos t 3pocrae' gl co" 51- -" 3 t o, sa apoMixKy loi trl y = cos r crarae.'49 583. 1) sin 190" sin 191'> 0, sa npoMirtliy [181'; 270'l y = sin r cra{ae; 2) cos 1300 - cos 110" < 0, Ea lpoMixrcy [90"; 180'] y = s6s .t saags.. 584. 1) sin 58" > cos 58'; 2) sin 18" < cos 18"; 3) cos 80' < sin 70'. 585, 1) cos (r = 2 sin 25'; sin 25" - O,42i 2 sin 25" = 0,84;0'84 € [-1; U; piBEicrb 2) sin cr = JtcosSs'; cos35'- 0,82; .,6cos35" = 1,16; 1,16 e [-1; 11, pistticrb /-546- l ) , = sin l x + : l - 2. ' 6.) nocmnoBHicrr, tro6yAoB[: 1 Y=sinr; t'nlr.z. y = ernl,r + 6Jr nrBop!.r Ha 6i 372 ill: AITEEPA Mep3rrK A. r. ya iH. A€aeMirBri piBeHb ii'::i'iiiili::i:.:i ysns Ea 2. , u=-;*",,-i). locniAoBnicrB ro6y,qoBr-r: ,., = *"['-*,), trpaBop]n{ sa sez. t) , = -3"r,'(r - 1). nocrdsossicrr noey,losa: ,., = "t'('-;), op"uopw "u f ; 3. y = -B "t"[" -;), poarsr ysaoBxc oci oy. zt r=-"("*1) -r. rroc,riaoB'icr' no6yaos,n: 1. Y=cosr; ,. o = *"1'. X),,riuoow',u {; ::i!i:iil:ii{lil ArrEEpA Mep3rrKA. r. ra iH. AKaaeMieHrr piseHb irl: f _ 3. y=stnlx+il-2; t D-/ I r, ol 12l 1t 6' , , = - i -"(, - t), crncxas', ao o, y 2 parr,. 373
  • s) y =,6""-; _r-...--; D(g):cosr_l>0. ; I l #ffi 6) a) 6) # I;;;:;:i::: D(v): B; v = c.s r + cos irr.a)cosr>O.,,_" 6icosI-0'-'.osr: 2) 6) a. r_"."(,*l]=r. *u" ,," r. 588.tr,,-/r->rz, _ , vsrn x, : Dtg): sin y,6. r.. [2^n; n + 2nn], n e Z; g = sint. seg' t) v - (.["",-)'; D(r): cos r ] 0; y = qos .r. ,(y)j -cos,i:0i '=Iroo'n.2, cos.r a I: r = ,--^4. n EZ- a) ,r. o: ,, = -,:': r'1: ,{J)i,er u, -. 0,, _",1 I lill,i;::i:,, "t '"' r - srn "r = 0 Dlg); -sin" > n. __ -",^=nn, 1 37a i_l:,:, artaa""o Mep3aqK A. r. ra iH. AKaAeMieHrr, piEe,rb liiji:iii:_::l_i::iiji 375
  • al j/ = Gin'-; r(v): sin,- 1>0; sint>1; r=f,+2nn'nez; b) y=bgql; D@): cost+o; x+f,+nn,nez; a) cost>0;Y=1; 6) cost<0;U=-1 590. 1)y=sint+ l;D(ulxe Rl a E(yr: lo; 2l 6) syni OyEriqii: x = -! +2nn, n eZ: tn :n-l Bt s ot x Fl-!;- 2ftni; ' 2nn )' n e zl rf y spocrac. rxeo rcl |,znn:|tznnf.ne z: u cn*a.-' L """{" *'l; ' znn: !r' + znn l' n e L; A) y.",=2 npn t=!+2nn'neZ; y '=0rur x=-L+2nn'neZ; ,, r="'"[,-l), D(y),re Rl a) t(u): [-1;1]; 6) Hyri OYnKuii: '=f,'"'''-z' "'tv'o; x e(!+ z^,;! +znl, n.zt I < o; 'ce( | * zn':f,* zn')' " 'z; r) y spocrae, snrqo '.l-f,* znn;! * zn')' ''z; v " t '' ***. , . f 1! * znn; -It znnf' "2; 376 iril AITEEPA Mep3neK A. r" ra iH' AKaaeMiqHnr piBet" illilt'i:il'tiili A) y-",= l npri t=-?1+2nn,neZ; y-t, = 1rp4 t=-!+2nn,neZ. 3) y=sin2r; D(u re R) a) t(y): [-1;1]; .no, nym QyExqr: x=n,neLi 1,. B) y .0, srqo 'clnr;';-nn)-n-zt a-o,sttl'o f--l rt y 3pocrac. -- -+-rr," nn,nczi g cralac, L4 4 ) ,.1f,*nn i{^rn).,.r, ot '.1f,*n,!*nnl,n.z; 9... = 1 rpn t=!+nn,neZ; V.,"=-1 upn ,- !+nn,oez. 4r u = -f sin,r: Dtutt x e' R:'2 ", t,,,, [ !,1l' 6) Hyni Oytrxqii: t=nn,neZi B) y > 0, s&rqo r € (-n + 2firy 2Mt), n e Z; A < 0, aRto t e (2r1ry jt + 2nn), n e Z; f- I r, , ipocrac. xel':"znn:'" tzrnl.ncZ: g anaaac, f - - l xel :+2nn:L+2nn),nez: ol v*-! npu x=-I+2nn,nez; v-,,, = -t wu r=|+znn,nez. (n lx.l,- + ftni n +,rn ). n ezi i:liilli:iill{ii: UTeSPA Mep3ncKA. r. ra iH. AKaaeMi.{Hr,rr pieexs i{:J 977
  • 1 591. 1) r/ = cos .:r 1; D(y, x e R: a) x(y): t 2;01; B) y<0,sriqot€ (2nnr 27t + znn)' ne Zi r) y 3pocra€ rpr r. € [-n + 2fi,zfin'l' n € Z; ycnaaae' mflqojr € A)y,,,,,,=0npta,=2fin'n'z;a,,,= 2 npi x = 1t + 2nn' n e z' zr u = cosi x-l']; Dru;:, -R." :1) a) E(y): [-1; 1]; 6) syri OyEkIIii: x=f,+2nn,neZ; B) y > 0. snrqo,.( I r """'i*2",), n ez; a < o, ",.*. ' -[i znn,,! znn.n. z, b r) y spocrae, '.1-! *z^,, !*zn)'".2; v." t", '.1 * 2n,,4 n zrnl, n. z', l3 ri I r) v.", = t, r= - +2nn, n eZ; zt y=""'|, DQrxeR. 4a=3cosx;D(atceR. ,[, "''/ 1 '/ t(v): [ 3; 3]; HyniflHxuii:, -;,",. ^ /' y o. ex,xo x.-'r -znn:')'r,,)., -z: v o. l- ',.." ".1; z"^,"r' z*,)., -2, r) y 3pocra€, x e I n + 2nn; 2nnl, n e Zi y cnaAae, r € t2nni n + 2nnl, n e A) y.",=3, t = hn, n E Z; C,,,",= 3,r=n+2nn,ne Z. 5s2. u 2ain(zx nl r, -o,,,,*- n." | 3t " nocniAoBHicrE ro6yAoBr.r: a) !, sin 2.ri / n) br y=slnlza+-J. yniBoHa : z; o r=r"*(r"-f). po3rsr y3Ao',,. oci oyy 2 pa3r; .r r=zs"(z'.lJ -L yri,,s sa r oatrE,rr'. (, -se3. y=-3sir,l;- 6) 2t Dtsttx- R. IIocniAoBnicr6 no6yAoBr: ar Y=sln_ - (, rl n ul , srn-" 2 6) " " 6 :::!iii:::iiirti* AIrEEPA Mep3nrK A. f. ra iH. AKaaeMi.{Hxn piEeHb lii: 379 l2nni n + 2nn7, a) 6) ') $$,ffi r = 1- 1 = !l 12nn. r .7. a) ,s(y): I 1; 1l; 6) Hvni Oysftqii: t=fi+znn, ne Z: B) y > 0, sl{qo r € ( 7L'r 4nn1 T + 4nnr, n e Zt Y < 0' FKUro r .- (n' 4fn. 3n - 4rnr- n I zi r) y3pocrae,t€ | 2n+ 4nni 41Lnl, ne Zi v cnaAae,:r € f4nnr 2n + 4nnl' ne Zi A) y.", = 1, r = 4nn, n e z: v,,,u, = -I,r= 2n+ 1nn, n ' z' 378 li::: AITEEPA Mep3nel< A. f. ra iH. AKaaeMi'{Hlri piBeHh :;:::;::::::::::::l:::ai:l
  • 3) , = *""(; -;), posrnr ysaoBx{ oci orl v 3 pa3r'; , = *",'li -i) , 2. yropy Ha 2 oA{'sqi. Ma€Mo crrcreMy piBIIsEb: l+x *_"^ t- Bc u '"' ;=ro'1v , 1 i: -___- = t0; lx l5r " u+ lu 15u+2-15 PosB's*ieMo Apyre piBEsHIIs: 60(16A t2l-9O0s ,^- 900y.120-900y-150y-20 ^ -150y-100 ^ tbvl '* 1br+, =u: -u+2 =u: 1,, _ roo t.. _? 1s0e - 100 , 0. ' 150 1' " l.r = a0' ts .2 / o: ' n. Ir-|' Io"-r5r Ly+-1b: BiAno1iAb: 40 *M. 5. BnacrraBocii i rpaoiKn OyHKqifi y = tg x i y = ctg x 5g7.a=tgt tl "(-;,t)' r-ru(-;)' 1= 1; Eenpasrnb*o, ro,,*al ,,e Ea'e*c'rb rpaabiriy 4yHrcqii; /-/-2r Bl-;'-Js]t -ft =tc[-;], -.,6 = Jt, EpaBr{nElro, ro.r&a B rlanes.'rE rpeoi$y OyHHqiii 3) C (tr; 0); 0 = tg r; 0 = 0, npaannrso, ro.{xa C Ha,re)rcr.rrr, rpaoiEy Oylrxqii; ,, "[z'. Ja). Ja -,-zt. Ja , , '!l G Jjo,'[u,t,-B=tc;' - l =te['I-6J; -3 T."*"',"". roqRa , HanerltnrE rpaoi(y OyErcqii. 598.u=ctg, /- l) Al^:l]r 1=crc;: 1= 1, npa!nr!,'ro, rosxaA Eanex'{rh rpaoiky o}'Entrii; /o- /.-, z1 r] {;ol; o=ctgl }]; 0 = 0, rpaBunLso, ro..&a B Hsne}crrb rpa@iIcy O}'s- nqii; -^f 'v5) '6 rnr "EIt c[-u;fJr t=""[ a'J, !e=-n6, uenpaauarso, roqna c lr€ Ira,r$$&rr, rpaoixy Q]'Ercqii; ,r "(f; '.,4), J" = *r*, la = "t*[^ - iJ,,6 = -f , ""nn",""r.8o. roq&a , He lr8lrexinrb rpsoiky O}.IrRqii. 599. 1l Hv,rsMu dvgftrii u = crs -r c 1, -I, 3n, 5n, 2' 2' 2' 2) ne ra.rexarr o6.nacri BlraIIa.reHEs ibyr]Iirliii O: '1t;2it. 600. 1) HynsMs Oysxqii y = tg r e n; 0; 3n; 2) He ua,relxa rE o6,racri Brl3ua,rcHnr Oysxrii y te r: -Tt -X, |, tX :iiitli:iit:jll::i AITEEPA MepsIeKA. r. ra iH. AKaAeMieH r piaexr l{! ger r = 6Oy, oo-15 6o' = ro. l5a +2 x'-3x+2 594. 1) l(x) = :- . ; Jx=1a6ox=2, BiAno,iAb:2. r'z-3x+2 - l(x) = o; -'- --=u; [x'at+z=o, lir-1+01 Z f(x -,"[x'zli, ocrcingftg .r2 + 9 > 0 trpllr€ B' ro Ovgrcqis EvniB He Mae' BidroBidbi Ee icHylorb. s f(r= x',lii; D(y):r-1>ojr>1. f(xl = 0; xJt I=o; x=oa6o.:=1; t = 0 He saaoso,'lbHn€ D(y)' Bidnoeidb:1. 4) Itx,= J-lx -2t Dtattlxl- 2,0: lxl> 2: r c l -: -21- l2i +-)' ,!i'l i = ot lx 2 = o;lrl= 2; x = -2 ^60 x= 2 Bidnosidb: 2i 2. / 3a uru.r,It',"|=,il3"/ 2,.r0) lziJ .ro. I"i ,ili r. uri r zt -r:u] =zl .3{/ =21 3'?', 1032t = _: 2',.10" 10 5 !s tJ = 21. 380 :.iil AITEEPA Mep3rt( A. r. ra iH' AKaaeMiqHnr pieerr {ill{ll:i{:}}ilt '60"15
  • l!*n*,!*n).*.2, 2 ) 606. 1) y = -ctg r, crMerpis y = cts r BiAHocEo oci Or. 2') v = cls r + l, rapanerrr{e nepeHe- ceHIIn BHu3 sa 1 oArnlrq&. 60 l . 1) Ha KoErsoMy 3 rpoMir{tldB tg( 38") > te(-42"); 2n 7n 2) tg-. < tg-, y = ig , 3pocra€' or}ce, 3) tg 130" < tg 150'; 4) tg 0,9'r < ts 1,2n; 5) ig 1 < ts 1'5; 6) Ha lior*{HoMy 3 rpoMiJ{KiB (rk; tr + fift ), & E Z v = cig n cnaAae' or]rle' ctg 24" > ctg 28'; r 3r! 7) ctcT - cts?: 9) ctg 0,4r < ctg 1,4r; 602. Ha (oxcsoMy 3 npoMi,rcxiB ( !*"u,|*^n)'o'7' u=te' 3pocrae' Ha t{oxi' HoMv J npovixKrB lnftl I rh, P - Z 4 clg 'r claAac o-}t(F: ( nt 3) y . rtcl .r + -]. ndpa,rpnLsp nppFHecFtsFF Br iBn tsA 8) cte ( a0") < cts (-60"); 10) cts 2 > cts 3. 603. 1)ts1,2;ts0,9; ts0,5; ts( O,4t 2) cts 3'2; ctg4'6; ctg 5'3; ctg6' 604. 1) te 1,6; tg 2,5; tg 3,6; tg 4'1i 2) cte ( 0,?); cig ( 1,4); cts ( 2'4); ctg ( 2'8)' 605. 1), = tg t' clrMerpis rpaoiria y = tg :i] BiAEocso oci Oir' 2) a =tc t + 2, n^PanenEse repaEecei' EE lrroBEt oci Ov IIa 2 oAIrHErrl Bropv. u=te'+zl li /! I n1 s = "tc|,, po:r.sr yonosxr oci O, y 2 pa3u. 99 607. l)sino ;1980': -ts80"-3.78:3.78a I li lli piBHicl6 /p vo}t{nuBd: 21 costt= ctg!; ctg+ - cts10'= 5,67; 5,67 e l-It 1l; piBHicrb IIe Moxnr.rBa;"18 -tA :r coso rgf : 1gtr = tg20'" 0.36:0.36 - L r: Ilr pisHicrb vor(,lrBa."q "q 608. 1) sin 78" < tg 78', ocrrinbKn sin 78' < 1; tg 78" > 1; 2) sin 40" < ctg 20', ocl{inbK]I sin 40' < 1; cte 20'> 1. ::::i:ii::l{iil::i: AnrEEPA Mep3ncK A. f. ra iH. AKaAeMi.rHrar pirenr liilt 383 1) tg 110" > te 90"; 2n 5n 3) tg- < tg -; 5) ts (-1) > tg ( 1,2); o, = *(' - ;), napanerr.senepe'e' celinn y = tg r BnpaBo Ea t. 2) cts 100" < ctg 92"; 3JI 5n 4) ctet > ctg -: 6) cte (-3) < tg (-3,1). ii ,l 4) g = te r, crlzc( YsaoBri{ oci O, y 3 pa3lr. I y 3 pa3lr. 382 i::::: anfEEPA Mep3ncK A. f. ra iH. Al(aaeMi'{H}ri piBeHb :::::::::i:::a::::::::::::::
  • ooe. rl v = *c(, + 1) + 1. rlocniaoBriicrb ro6vaoBll: ^, a=ctgt: /n)It 6) y=ctgl,rr -], $aparFnbHe nepeseceHHfl BnrBo Ha 4: / E Br I ctclx - ;]. t, r.ear-*" ""penecelrHn Bropv Ha I zr ,="t"[s' Il." " t2) IJocniAoBHicrE no6yAoBr-r: a) !-cteI' 6) y - ctg 3r, crucx yeqosx ociOrygpasn; / _ st z=ctsl sr l:l" - 12) naparlenbse nepeEecerrEf n Brlp3ro Ee -. n "Ls 2x-!. nocnjaoBHicrb no6yAoBr.r: g=tg,;i U Lg 2x..'tvc!r y3rcs}l{ oci Or Y 2 Pa3x; u lgl2x ^ I, napaienbse nepeFeceHE{ ft BflpaBo Ha t ( 27t.r 61o. l) v = 2rcl.r''; J. flocniaosHicrb no6vaoBx: a, a =te 'i/ 2nl 6) v=2€l.r+;'J, napaie"lb'e nepcHec.IrH' sriBo Ha / 2n Br s 2tslx'?J. n*'* v"o.'* oci ou v 2 pas'l' 2l a) 6) B) {: ,1 zfi .-i +!+nn.,ez.2 tg'z * > o; or r. ry y = (ur"te")' , - lx*nn,neZ.L ut:1" lctg r 2 0; g=ctgr. 2t v=tsx+telrl Dtut: x+I+nn-nez: a) r>o;y=2text 6) x',oty=O. s1 y = .!,ts";; o1yy. y=nk,hez. L: 2l ctsxl ^ur. )x*n+nn nez, lctg r * 0: a) y=l,nllqoctgr>0j 6) y = -1, snqo cts: < 0. ;:i!:iiflifiltli AITEEPA Mep3ncKA. r. ra iH. AxaaeMieHr.rr piBeHb ll, 385384 ii:i AITEEPA MepartK A. r, ra iH. AxaaeMiqHnr piBeHb :!:lli::::::i::ii:il
  • T 612. 106 no6yAyBarr rpaoiK 6vHKqii, Eeo6>riaHo: l. 3Haiire o6na.rb BrirHaqFlrHt OvHXqii: 2. BlrKosarr'I Heo6xiAEi reperBopeEHn' po3Kplrrlr MoAynb' spaxoBvrotrt rpoMr'{rfttl' IIa sr$rx niAMoAyrl]'lrn ii Bt'Ipa3 Ea6yBae AoAarErx ra BiA'€Msux 3HaqeEL L lr q (Jre*l i 1sx--oiDtat: nn::' nnl'n-Z 2) erqe oci Or - 6e3 3Mislr, Elrxtqe oci Or - crMerpis BiAEocEo oci Ox. i 2, a = cte r ctg lrl; ,(y): jc + nn, n e Z. Po3rnsseMo ir > 0. I = ctg ir cte x; a = O. IpaOiI.oM rDyHRqii;a npoMir{Clv r. € [O; +*) e rpsMa, slia 36iraerEcs 3 Bicclo O'' p.""""""..'t < o. v=ctg* ctg( x)i a=ctgx+ ctg t; y= 2 ctgt fpaoiKoM OyHl{qii Ha .tpo*i*"v t l (--; 0) € noraHrellcoiAa, po3rsrHvra $AoBtrc oci Ov fpaoircoM OyHRrrii € MHoxclllia roqox is xoopA EaraM 1t u '"' ' 1*' z "n'n' '' otl, ''"!,,.2.ts r' ltg,. - 0, l' , "^. ^ .2' z po3r.lsHeMo te' > 0.,.(."u, !, "o, u. t). a = ffi' v = t. rpaoi]{oM e rp.aMa, napanerbHa oci Or. p*rr'n€Mo tg ' < o. xe(!+nn;n+nn,u.t). ,= J81, o=-t, rpaQikoM € npsMa, xaparerLEa oci Or. 5) u=te*+Ec: D(a = R. a = rg ' + lte rl. Pogi'nrHcMo tg .ir - 0. .r -ln^rt^r,^.71. u Lex I re:tiu 2tsx. LzJ fpaoilloM OyExrtii € raEreEcoiAa, po3rsrHyra B3AoBrrc oci Oy y ABa paslr. Pos!,lslreMo tg :c < o. " .(! t nnt n * n,, o . z). v = tsr - tc ,; v = o. fpaoir{oM rbyH(qii € npsMa, sl{a B6iraerEcs 3 Biccrc Ojr. s) a="te* J.tc.";; D(g):r+n+nn,neZ. y = cte )e - lcte xl a) ctgir>0,y=0; 6) V = te x. D(y: !+t+nn,neL. (;."",".',") Zl v = [.te; -ctg'x > 0 Bllnoiiv€rEcg 3a vMoBIr, rqo ctg't = 0' r ! ^^., -z: Dl!:)'nn.n-7t npu x L nn'n-7t a'o'^2'2'2 386 :;::::: AnrEEPA Mep3neK A. f, ra iH. AKaaeMi'{Hhi piBeHb :a:::j:::::::::::::::::::::: 6ry ictgrir Dtyt:! ' nn.n-2. Cro.rarKy 6yAy€Mo rpaoiK OyHKqii y = tg n. t{acrnlry ryaoixa, slca 3Haxoalrrscs sx*{.{e liA oci Or, lino6par{a€Mo cnMerprqHo oci Or. :::::i!iii::iitli: AIrEEPA Mep3nqKA. r. ra iH. AKaAeMiqHrt piBeHh l!,1 347 lt* . rsr ,x-F--nn,n.L, l-,1 "^,,.t,1J a=Li | 2 I 2 ts r' ltg,. - o, l' , "^. ^ . z'
  • r 613. Hexafi a, = -4; a,=5.a,=o,+6d;-4+6d=5',6d =9; d= 1'5; e,= -2,5i at- -l' a1= 0'5t tt|= 2i a6= 3'5. BiAnoqiqb: 2,5t -1; 0,5; 2; 3,5 614. Hexafi b1 = 256: bi= 1. bi= b1 .l 1- 1 q'= 256, qr=- 4 aoo q,= 4' BiAnoqiAb: I) 64:. 15, 4i 6164: 617. 1) I+cts'5d=--: ; srn- 5ar _Cl ^. 3 3 C lq3 3) ctg' 1; 4) 5) -(t- sin'o) - cos'cr - I _ ----;----:+l=- " tl ctg'c+l= -(l - cos 0, sin c - sin? cr' i sincr cos cr L': / cosc sin a ':ii:.' . | :ra.::_:, =sin.o rcosru =1; cos.r I / sinfl 1 I - sin Cr sin' (I sin) n sin/ a 1-ctg?d{l-cos':o) - cos'c sin':c I cos)o sin'a " 'sinc I ?) -+ - ts'20 = 1; 8) ts, p + 21g P.cts B + cts,P- (te,0 2 te p.crs B + ctg, B) = = Lc'1 9 + 2 + ctc, B - tc, F + 2 - cte, F = 4, ore. rr lll -l - vr3 I | ,13--!, t4 , t. '4' 4 ) 16 16 16 16 He BrzrioHyerlc.fl ocHoBHa Tp{roHoMerprrriHa rorollEicrr, sin2 lx + cos, (r = 1. Orse, piBllocri oAHoqacEo Br(onyBarncs IIe MolcyrL. 2) 2,5 - 0,6 I ,5; 1,5 ' 1. He BrrftoEyerBcs ocHoBEa rprronoMerpaqHa rorox{EicrE tgs. ctg (1 = 1. Orx{e, pi4nocri orllo.racHo Br.rKorryBarscs He Moniyrb. 6te. r) l2l',131'=1*-s -13, 13,r. 5,/ !5,/ 25 25 25 25 PiDHocri Btrt olryBerscs se Mor*{yrb (arB, no.ncHeHH.s Ao saBAsEHn N! 618 (1)). 4 1 45 5 5 2l - 7-= +l s 4 94I I PiBsocri Br.rKosyDarrrcs He Moriyrr, (ArB. roscHerrl1n Ao aaBAanH.tr Ni 618 (2)). 620, PiBEocri BfinoHJ,.BarIIcs se Moxcyrr,, ocKinr,trlr sin, d + cos: (x = 1. 621. 1) 'firiqo tg dl > 1, ctg ol > 1, ro tg s ctg cr > 1 2) filrnro lts dl < 1, lcts cd < 1, ro tg c.. ctg o < 1. Ane tg o ctg q = 1. OrBe, HaBeAeHi yMoBr.t Blrr{oHtBarrcs He Mo)r{yrb. 622. ll I 2rgq . Lg'a' I -2tgo r tg'n = -J- . l" J-, cos'Ct cos'd cos'ar 2) (sin? s)' + 2 sin'? c, . cos' o + (cos, s), = (sin, d + cos, ci), = 1, = 1. 3) sincr(1-cos) + sin c[(l + cos) , sins sinocosc[+ sinc{+sinctcosd _ ' (1+ cos)(l cos c[) 1- cos' cr 2 sin d 2 = "i;t; = "i" "; r cos0 sin0 cosoll rcosl .sindsinc '' .ino-f*"o"o "lnaft*.o"f coad+cos-0+srn'ct sin (x(1+ cos d) cosd+l 1 = "i""O + "."a = "t"; iiilll:*l:liii;.1AITEEPA Mep3rqKA. r. ra iH. AxaaeMiqH.,rt piBeHb ,al:! 389 .qa;256.4=1t 16;4. 615. IIpoa]'rirnBtricrE Itirbrcicrb sacy ItirrbLcicrB aeranei l-it podirflnl! Ha 3 Aerani 6inEme ---1 na 1 aeH; 90 Aeraneii 2-i po6irl Ic 90 Aeranen Hexaii Apyrdi po6itEr'Iri Br{roroBnsB x Aeratefi 3a AeEE, a trepEtIi - (t + 3) Aerui ra aegb. ncpu{fi po6irnrR rpaurcBas 90= .*"i". u apv,,ii - 9:0 a"it n"pt"; npa(loBaB sa I nesb Me$u,e. r + 3 90 _ 90 - r. 90 9.L I O, 90x . 270 90x - x' 3-r O. a xt} -' x x+3 (rr3) x'-3x t27o n. f-r-s'.270=o. {-l} x) Bx 2ro=0.,D bt-4oci r.(.r - 3l lr.{.r + 3l 7 0i I D=g-4' 1 (-270)-1089; - t-38 3,33 , JD = 33: x. = ;-;" = 18. I'e 3a.ooBonblnc vMoBv 3a4aqi: x,' z ;- -15' 15 aerarefi qoAHF BuroroBnsB Apyrnii po6irl{rK, 15 + 3 = 18 Aera"'rei BnroroBnsB neplllHii po6irFsk. BiAnosi)b: l8: 15. 6. OcHoEHi cniBBiAHotxeHHn Mix rpnroHoMerp[qHrMn OyHKqicMx oaHoro r Toro caMoro apryMeHTa 616. lr iin'o: 2) (1 - sin'2cr) = cos'? (1; 3) 1+1=2; 4)1 (sin'34 ' cos' 34)r I l=0: st "o"3 og'c, .os.i sind 6l - = srn d- 1 coso 7) 1g' di . cos'a sin" d al .os'd r =cos-d lcos g zcos (,; sin'.l I " / 1 ,) sr -"'o [ .i, cre aJ ' cos'c-r {l-ros7cr)- -sin7.r; ro) 'i":q !e#=r cos" F $n' p "x11) 1' sin't = 1 sin'- = cos- ' 12) sin'zo + 2 sin d'cos s + cosr o + sin'z& - 2 sin d cos cr + cos'z= =2 sit" d+ 2 coE2 ct= 2(sin'c, + cos'?d) = 2 1= 2. 388 lrj AIrEEPA Mep3nrK A. r. ra iH. AKaaeMiqHni piBeHb i::itiiiiiiiii{::i l I I
  • il 5) (1- sinoxl + sin cr) cos'zcr' - 1- sin' cos" cr - 1- (sin'+ cos'o) - cos cr(1 + sin q) cos a(1 + sin&) cos s(1+ sind) sin'+ 1+ 2cosc, + cosd': 1+ 1+ 2cosc (1+ cos s) sin (} (1+ cos Cr) sin q , 2+2cosa - 2tl+coss) 2 , (l fosslsind {l cosa)sind sin0 sins sin P -. cosd cosP sin o cos B + sin 0 cos n . coscrsin0 -sinocosp . " "*o "o"g """".*0 sinssinP sin d sin B tsin o.os ll + sin p cos o) sin d srn 0 singjlnll rsorsBr cos s.os ll{cos o sin p I sin Gcosp) .osocosp ^. taSa (1 ctg':3s) tgSq ctg30 sr ffi ,rr;-**....-= " cos o /sina cosa) coscr 9) -.1-+- =-:sin a cos(l srnc / sln s cos rr cosd.srn(I sino l 1or _jiny _siny-cosy.rosy siny_ {liny losy)cosy _ctgyi --' 1 sin'y sinY cosY srnf {srnY-cosYr 11) cos'zd(cos'9s 1) + sint cr = -cosz .t(1 - cos2 c[) + sin2 s = cos2 o sin' d + sin" ft = = sin' ct(1 cos' o) = sin: cr sint a = sin{ ct; 12) sin'd(sin' o + cos: c{) + cos' c{ = sin'9 s ' 1 + cos' d = 1; t3r cosct-coso ig o cos.r{l ts? ct, "'i* aj.* = ""1r,r sinB - l- sino sin0 1-sinp+sinP 1 14) p - tclr "".0 .,=0 *"p -"F 623. l) r 2cqll-cte,9-1 2ctsp cts ll- ","t pt ","t p="r,i"p' 2, sinzd cosr,rtts s rl+crg'd+1) "t" " """'1J,"-;"',") = =sin2n+cos2s=1; ^. cosB(1- sinP) + cosP(l+ sin B) r' -- li+ sinBxl_"'nBJ 2 sinf, Ein x(l si n r.) --.-_'' cos r. i I sin r cosr.(l - sin x) 1+ sin, 1 sinr+sin':c+cos?:r cos r(1+ sin t) cos r(1+ sinJr) cos r. ", "." p:rgrp:lr -1414--9 n p) - cos'p- I 2sinp I sin'p "' ( t - sin o)cos P 11 sin0lcoso _ 2-2sin0 2(l-sinpr 2 - (1 "lr' P)cos P - G sin P) cosB cos P ' 39o . ii*: AJTrEEPA MepsrqKA. r. ra iH. aKaaeMi'{Hr4i piBetr i:.:ililillliili:j 7') tg'q(1+clg'?0) _ te'a+1 - 1 (1+ tg" o)stg" c[ ctg'c, + 1 cos'9c[ ' I "'"cr) /- sincrl cosa+sina coso/ cosc/ coscr 1 sin': a -=-=tg"cl;. sind + coscl (cos.x + sincr)sin s _ cos q(sin o + coso) = = tg(x, 8) cos'z d(cos'z d + sin': s) - cos, 0 9) sinz d + cos'zcr(sin? cr + cos, c.) 10) tg c . cte & + sin? cr = -1 + 1 624- 1t IInHn: adsa = . '2 SHaiLmu: sir. a; lg d.; cLg cr, sin'/ ci = 1 -cos'? c; ",no =.,,[ -.odo, "'"t -r[l "ino= $, rr"= +,;, tgc'=-!5. *eo=*o!, a6osino 6: ,rt=f,!, rscr=.,6r "igc=f. 2J AaHo: sino 0.6' tr. o.n. SH,aLmu: cos ct; lg s; ctg s, "o"o=t.,[ "irfo; "o"o=-',/i-O,6" , octrinbrr]r c, - Ryr II qBepri; cos tr= 0,8; 0-6 3 4 r tso : cts(l - - 1--"0-84'33 cosF cos 0 sin 0 + cos 0 + cos F sin F 2cosF 1 sin'z P cos'p _ 1+1 2sinp _ (1 - sin P) cos B 6) cos a(1+ sina) -. sin'z- (1+ cosa): ' (1+ cos s)sind - 1 = cos, d . 1 - cos, Cr - I = 1: =sin'9C[+cos'cl.1=1; sir' cr = -(1 - siD' cr) = cos'zd. "6.3' 3') ,qaHo: te a = - SHanmu: si[ &; 3rr 2 cos d; ctg.q. lI"II "tao E, "o",o r, tg'si cosc/ rr/l ,t,s, ocftinr,&r cr Kyr III .rBepri; *""=-,F= * ./5 l) $ noxo: ate..=-! i !4<a.:". SHaiLmu: tg qi sin st cos a. p,s 'raHHs: t'o = !. t'o = q 'cta0'4 1+ ctg! o; sino=t ocRi,'l6rair c[ &yr IV .rBepri. :tiitttitl::i:lt: AnTEEPA Mep3nqKA. r. ra iH. AKaaeMi,rHr,rn piaexu .r:l!: E 1 "itf " = 391
  • q ""so = uii:1-6py = 16 - s,a6 = ."f0, el = o, s. 12 n 625.1 AoHo: coscl=- i u < d < -. S'ailmu: Ein e; tg 0; ctg cr. "i,'o = t.,/illll'o; "i'o - ocRinbKn c. t(yr I .rBepri. '12=5 ' .tno=12 =2.E,13 12 ' 5 f 144 E{ s srntr= Vr -=11*n=ra, ,,6 zn 2) AaHo: si,ncr = i It < ct < t. SnaLmu: cos ct.; tg ct; ctg &. "o"s = 1J]_ "ir,'cr; pess=- I a r'iT Jr a Ja r ,[5) Ja "6,roscr t-*== t/,u - 4 : reo - -:l n l'ffi= rei "/1t "6,J33 3t naHo: tlct !, !. ".r* SHai.Lmu: cte &i sin (}i cos c(. .tgs=-l r cLEd=-3; 1, =1-ctg'oi sincr=-- tg q srn- cr ",'"= f t.'-, ocki,rlxx d - Kyr tv.IBepri I + (-3)' L 1 ,,[o srnc = ., , "o"o = -.'fi *in o; 110 JIo 10 tr a 3u4o !10 Jto 10 4) aHo: ctsa= z i !<a <n. SHaitmu: Ne $i sin ct; cos cr. teo = -L, te" = 1= -1,c[g 0 "r"o = E. ocxinl,x,, c !l+7' titto sina ,/_' =-L--'!1 | cosa=r'[r sin,c; !50 5;2 1O f ,il | 2 7,[2 coso .j1 -:'I lr .1 ! L rol !- loo ro 626, IIlo6 4onecrn roroniEicr6, Eeo6xiAno BnRollaru roro*cEi neperBopeHss olHiei a6o ABox 'racrrjs rt oAepr{arr oAHarioBi B!rpa3r-r. Mon {a cKnacrv piafir.rqrc niBoi ra trpaBoi qacrfiH ii oAepxarn r0r. 1) BIrItoHaeMo reperBopeHEs niBoi .racrlrEn: (cosd sir(xxcos'cr + cosC[sina + sin'o) - (coso sinoxl + cos(lsind) _ l- sinocosd I -sinocosd y pesynr,rari Mlr oAep,Iianu piBHi Brrpa3rr. 2) cos'd+sin':s sin'7c+sir'zo!g a=I sin'rr{I-rg:o,,t- ftit" "#= =1a19'q=-l;cos,o sin'n ^ / I 3) ----.- sin'(}=sin'o --ll sin':c tg:c:cos-d .oc'o l -. "6 z"i,'o 1+2coss -' z-"o-r 2sinc+Js (.,6 -2sino)(JE + 2sins) - (1+ 2coscrx2coso - 1) _ g - 4sins 4cos, d + 1 @=e"*"_1)12"-;16= l I i :.:.; :.:.:.:.1 i:lid cos' a ctst a = ",";*.i""", clg d 'Lg'o t cLg'?ol ctsuc: 6) 7 L=t+cts,q; sina = I Ryr I1 'rBepri. _ 4 - 4(sin'? o + cos'? ct) = 4 4 =n. 12cosd lX2sin(l r Je) rZ"o"o l)(2sind + J3) "' "( 1 cos" 0l ;--- r l sm-c ) ;;t'- : l cos'd/ 5) "tnt' "o"o sinocosc+sinc -- srnotcosd- lt.l sin il I cosc cosd coso(l + coso) . sirr' a 1 +.Lg' c( cos' a ::+- cos? u = I -.tg, n cos, c - sin2 c = "os, cclg, ct = = cos' o|t I t ctg'd) = co", o .1 - "."r o. sin'.r 8) "i""a,f""":"__..","J "f_g. sin,o sin.c _srn,cL sin'cr / I cos, q(l - sin, d) cos, cr . cos? ry - ros. o = tln a. 627. 1) sin'zlI cos'c((sin'ztl + cos, (r) = sir, c, cos, o|; 2r H#--"." "*,of t, - - 1 | = .os, q . c€^ a. qin'd ) ,, 1"i.lo -"r",ol.Ie'g. sin'/otl cos'?d) cos"c "' lcos'c _ " sin'c _ "oa'o sin s";n.o = _sin'?csin'o cos'a ,. cos- G srn' .I srn_ rl llilli;::jilltiii ATTEEPA Mep3rqKA. r. ra iH. AKaaeMi,{Hur piBeHb llil 393392 iii: AJf |EEPA Mep3neK A, f. ra iH, AKaAeMi,{Hnt piBeHb ::l::::l:::::::i:l:::: i
  • 624, 1)sin{cr(1 - sin' o) + cosa o(1 - cosz c[) = sin{ d cos2 Cl + cosl o sin2 o = + sinr cr cose o(sin' o + cos2 c!) = sinz c cosz d; 2) (sin'zd)3 + (cos: o)3 + 3 sin'?c(cosr q = (sin's + cos? dxsin{ c - sin2 o cos2 c! + + cosi c[) + 3 sin! o cos2 C[ = sin! C[ - sin'? q cos'? q + coa{ c, + 3 sin': ct cos': ct = = (sin1 Ct)' + 2 sin' c cos2 cr + (cos1 a)'z = (sin? cr + cosa a)'z = 1'?= 1. 629. 2(sin'? o + cos' sxsina c[ sin' o co€'? d + cosa (x) - 8(sin! o+cosa d)=2sin'rq - 2 sinz ocos2 cr + 2 cosa o 3 sinr d - 3 cos{ (t= sina d - 2 sinr Cr cos2 s - cosi o= = -(sina Ct + 2 sin2 o cos2 ct + cosa q) = -(sin3 d + cos'? (r)' = -l! = -1. 630. CxoprcraiMocs ocHoBrrom BnacrrBicrro Apo6y: st qo qucer6HxR i BIraMeHHrIx apo6y roairtrrr Ira oalre i re ca e qncno (a6o Blipa3), BiaMisse Eia Eynt, ro 3sa- qesrrs apo6y Ee 3MiBr.rTEcs. 1) lloAirsMo ql,rcen6HfiR i aHaMeIrlIrrK sa coa ct: cos -cosd_tsu-1 _( ,. -rl,(, * r) ___r, n __t. sind cosd tss-l 3 ,/ 3 ) 3 3 2 2) IIoAin{Mo q cenl,nnx i 3HaMeEslIx l{a sin2 cr: 2cos'n ?sin'o "i"6 - "itf., zcte"a-7 _ 2-(-2)' 7 _a-7 - l= 0,,u. 3 .os: c . 4 sin a cos d 3cLg'zo'+4ctgo 3 (-2)'-4 ( 2f 12-8 srn- o srn- ct 631. 1) noAin{Mo qnc€nr,HnK i aHaMeBHLtIr Ea cos s: y IV qBepri: coE c > 0, ctg d < O, roMy cos o.ctg d < 0, "..o*cosc.coscr sin2o+cos2<l 1 1 sin (r 2) floainnMo qncenLHr.rR i sEaMeEHrrR lra sin2 c[: "tg1 =9,L iCl'l g,t, 9I 3,-7 -3 16- 12-r-s l-ctg's 4 4') 4 L t6r 4 16 4.? 7 7 u"r.,,@ = "t""' ". """ " r" a. "t"t ". "t" " "." " = .[."' " t r"t" a """ ". "t"' " = = r,6;" - "ir "f = bos o + sin al; q - xyr III .rBepri, roMy cos o < 0, sin (I < 0, cos cr + sin o < O. P$xpr{BaeMo MoAynb: -(cos s + sin d) = cos q sin c[. ". v6*'" -*d"*f 0 '1[oJ"{l*."'P) VGs,c"-lp coscs:npl. "' tcg.te" tep.tc" - tse"te" - tgp.tg"' cr - Hyr III qBepri, cos q < 0;0 - lcyr lI qBepri, sin P > 0; cos o sin ll < 0. Po3Kp{Ba€Mo Moaynb: cos s sin p : (tgpctga) = -"o"o. "inp, !9{. !in d = "in cco"F. sin lJ cosd r'"+" |]",Jr- tl "i,,o-.f,o *w,o -u"". "tno i"in, o -cos'a = sind - i, ,sin,o = sln a - lcoso.ctg al; q - (yr III a6o IV .rBepri. y III.rBepri: cos ct< 0, ctg o> 0, roMy cos(r ctg d < 0. 394 ili:AITEEPA Mep3nrK A. r. ra iH. AxaaeMiqHrai piEeHb iiitailliii:::'t 634. l)sin d + cos d=D; sinzc + 2 sin dcos cr+ cos2d=12: "ino"*o = b, 2 2) sinr a + cosr a = (sind + cos axsin, C[ - sin Cr . cos o + cosz d) = .(, ^t'rl ,(s-b') 2) 2 3) sin!c + cos. d=sina d + 2 sin2 c! cos2 o + cos{ Cr 2 sin2 q cos'o= (sinz d + + cos'tr) - 2(sin cr cos ctt, = -2.t-glJ- l-b1 2b'+ -l+2b'-b4422 635. 1)tg cr + ctg d = b; tgz u.+ 2 tg ct ctg o. + ctg! s= b2t tg2 &+ ctEz (r= b2 z; 2)-tg3 cr-+ ctg, o = (tg d + ctg dxtg, (t - tg o ctg ct + dg;a, = = b. (tg, @ + ctg, ct _ 1 = 6162 _ 2 _ 1) = 6o _ tr. 636. sin, d + 2 cos2 c[ = sin2 Ct + cos, d + cos? {x = 1 .t cos2 c,: -1 < cos d < 1; 0 s cos2 c[ < 1; 1 < I + cos, a < 2; 1 < sin, d + 2 aose o < 2. 637.3 sin, o - 2 cos2 d= b sinz 2 sin2 q - 2 cosl c, = b sin, 2(sin, o + cos? o.) = = 5 sin'd - 2; 1<sin ct< 1;0 < sin3 d < 1; 0 < S sin, d< 5; 2 < 5 sin, a_ 2 < ij; -2s5sin?d 2s3. 638. 1) <DyHAqir craAae, sl{qo 6inbuoMy apryMerrry BiAroBiAs€ MeEIIIe sHaqesds OyHIcqii. -. 7 7nexax. r >I /(xr) r_,: f(x,) ,,_-5. CknaAeMo pi3Erqro 3EaqeHB OyHXt-tii: 7 _ 7 =1xt-35-7x, AB_ 7(-x,t ,,+5 z,+5 (r, +5)(r, +5) (r,+bxr,+b)' I - r,.- 0i ,., + s > 0;.r, r b .0 npx;€ (-s: +-r;1r,1 _ L*,,. O. fla, < flx,1, orxe, gyE(qia cnaAae, 2) OyEKrtis 3pocra€, .EKrr{o 6inburoMy apFyMeEry BiaroliAa€ 6inLEe BHa.reHEs OyBnqii. Hexail x|- r,. l(xl)=6x, -x'zt fk,t 6t/-r:. Cxrs{eMo pisnnqrc ssavefi r 6ysrjrii: t6a, x:) - 16x, - xi t = ax, - t:-6x, xi =6(x,-rr) .G:- x:= = olIT rr) Ix. - xtl(J, + ir.) - (.r, xr)t6 (.r, - ,r,)). .r:-.r, >0i -t, .r, < 6. rovy 6 - (i, , i,t ' o. ' (,Y? - xrxb - (x? +:,)) . 0 npn.r € (--; 31. IQ,l - I(x,l ' 0i t'ta,t . lr,), orxe, OyHKui' rpocrac. ="1t'2)=" =/ tl =1_r t'= 1000 i 125/ .! ;; "': ( -9?5 I '= 4/roooo ro _, ' 10000, v 625 s - _ ^l D+DIgC 2 6 3tgd-7 " I " -5,5 2 80 ,25 _5 55 55 11 t:.:.i! .:.i:.:{ :::li:l i,i.iil 1 l I *,,, [#J' =1i",,] * = r"' nr' = 126t = t25. ,,[#]' f+J' r"n,t'=. i iiliii:iijiiilii AnrEEpA Mep3reKA. r. ra iH. AxaAeMi,{Hhr piEeHb !it: g95
  • 640. Hexan trepffs ApyKap&a ApyRv€ jl: cropilloR 3a roAnHy' a Apyra !l cropilror{ 56 3a roAtrEy. IlepIIIa Apy&apRa HaApynyBarla 56 cropilrox 3a roAr!I{' a Apyra - "o 4 "os"t. rr"p*u rr'Irpar{'a Ha po6orv ,," I !9 - !9 ] roan* MeHUJe' ro 3a vMo- g t a r) solo AopiB'roc 2 ro.au'a'. nppure prBstHHt ""*"*,t'09 tl t 5 Ilepllla Apy(apxa llaApyr{vBarra 5 cropiBox 3<r roAets' a Apvra - 4 croprEkr 4- ca ' roarn, 3a vMoBoro Bo{Ir Bxrpsfl'urti Ha 're oAHakoBufi cac' 54 Apyre piBssHEa crcre*", ;= ,, 4-P= z, ls, = +,, a x l_^ -^ 1o a 199 4=z,z; l-= I v x /sz n) 4n 3l cos _+ =cos =0: a al R 2 4) cos cr cos (cc+ B) +sin Crsin(d + F)= cos(c (o + 0))= cos (s - (r- p)- = cos (-p) = cos p; sjn53 cosT -ros53'sin?'-sin (53', ?') cos53"sin7"- slnOO"=4; 2 sin ((cr + P) - (cr- P)) = sin(d + p a + 0)= sin 2F; sin' (d + p) + cos' (cr + 0)- 1; sin l2O" 5") sin15' cos {10' + 5") cos15' cos cr eos B sin C[sin 0 +.2 sin ct sin 0 = cos (} cos p + sin d sin B = cos (o - B). l) cos (6d 20) cos 80: I sin (12" + 18") = sin 30' = ;r sin 75'cos 15" - sin 15" *""rU" = "r" uo' = @, cos ((d + P) (o P)) = co6 (q + B o u B]= "o" 2p' cos t64" - 4') cos60' = cts so. : @: sin (19".41'l sin60' - 3 cosocos B+ sincrsin ll- 2 sin dsin F=cos cr cos B siD osin p=cos(o+ p). 11 rsrfl_or= rsdr rep = 2 a i,l r tl 3.2 6 t-tga tgp r_1.1 8 L 8' 4 8 7 u = O.8. '2424, 2A 2A =I; - -=t1 0,6x x 5) 6) 7 8) 9) 644. 2) 3) 4') 5) 6) 645. 2a 22.4 O.8 ^ 5,6-0,8rr ^ 15.6 o.8'r=o' 0,8.r 0.8.r [x z u: BiAnoqiAb:7i 5,6. 7. OopMynra AoAaaaHH9 5.6y=_: x=t..u=5.rt, 0.8 641. 1) cos c, sos I - sin {, sin B + cos d cos [i + sin l:r sin 0 = 2 cos Cr cos l]; 2) sinSO'cosd+cos30'sinCr (cos 60" cos c[ - sin 60" sin o) = 1J3 l./3 i-"" - "r9"'" " - jcoso - f sin a' "6sin a: 3) E(sin Gcos45" - sin 45'cos o) I sin q + cosc[ = t; t. JZ v'"ina € tscosc-s:n,r r'osc sind coso-sincr-coso 0: 22 4, 2(cos60".oso r sin60"sina) J3"ino "o"o = ,t; =r r...a : v""inc-J3sina-costr cosd sind'sinc-coso=0 22 642. 1) sin o cos B - cos t[ sin B (sin (1 cos P + ccs d sin p) = =sin c,cos B cos osin P - sin c. cos B coscrsin P= -2 cos ct sin p; 2) sin 30" cos d - cos 30' sin cr + cos 60o cos c( + sin 60' sin o = r ,,6 t .,6.sincr ' coscr- slnc=cosc; -l n ft l 3l J2tsinrcosd-cos^sindJ cosd -sind = E-1r = lz v3coso-J2 -t'sinc coscr - sin..r -coso sinc cosc sinc=0i 22 643. 1) sin(d + 4(I) = sin 5cu l 2t cosl17" + 43'l = cos60'= t: 396 i::::: AInrEEPA Mep3ncK A, r. ra iH. AKaaeMi'{Hnf piBeHb ::ii:::::::i: :':i+'l 24 646. rsra Br tga - tsp 3--l = -3 = -1= -o-rzs.Iraotao I35 16 8 647, l) tE OA'+ 47", = tg60" = .,6; 2) ts (1" - 46") = ts (-45o) = -ts 45o = 1' B) I =--.1--=",nun"= 6, -' Le t27' 33') te60' '-'-' 3' o tel$.ff.)=te$=tel=r. 64A. D Le @4" + 36) = te 60" = 6; 2) tg tsd 30) tg 20. 649, lqo6 AoBecrr. roronisicrE,, roroltrHi neperBopeHH.s riBoi qacrnlln ri orpuMacMo s[par. piaHr.rfi Bxpa3y. eKIrii croirb y trpaBiii qacrysi. ,, cosacosp sinasin0 rsinosinp cosdcos0 ,. " ".. r "".0 *- r "*,p "* r "t"0 - "."""."0 - " 2t sin d cosp - cos(}sinp + sindcosP -.osdsin 0 _ 2 sin ocos0 _ rsocrsB. srnacos0-cososin0-sinCtcosB-cososinF 2.osos'n0 - ; ". 1E ros a - 2rcos 4 s.cos d - Ein 4s. stn d) Jzcosc-z "jcosn+z 'fsinc Jt - "' 2tsin45"coso r sinocos4S") ,[2r;.""- ^ Ji ^ J, . 2 -2aoscL- Z 2 sino Jzsind - ,,8 "o" o -.,8 "o"" - Jz "tn a Jz"in" = Jz "o"o , Jz "in c Jz "in o ,72 "o"o "sui :ilitili*.:::Jtit AITEEpA Mep3neKA, r. ra iH. AKaAeMi,{Hri pieexu iiL: 392
  • I' 4 5) sinr{a - pl {a-plr _ sinlo +rd-0)=!in2o_tn2o, cos((d-pl rld-pll cos{dt0 c-p) cos2o sin 45" cos cr + sin d cos 45" - (cos 45" cos o - sin45" sin 11) "iffi-.1, "E Jt lE . ;cosa+sina;- ms(I+ o ",na JE"ins ,12 J2 J2 J2 J2 cosa ' .6c n rsind SrnC sin s + 2(sin 60'cos d - cos 60" sin d) "i"o*z f*"o z l"n,, S *"o n 2. ]"1"o "6*"o sin(I-3cosC!-"jnfl 6"o"" 6-,--. 6".*,. "," "' J3.*t "'; rrtPu' ,("*€o' ;;;;ao' "- ") .f3 ".- -, *"P = ;, sinB = 1ri;: cos' P, sin ll = t16 fs s --.." t- 2b V2b 5 cos(n F0r=cos,rcos0-",,.ir"'"n 3f a) a ' 5' 5, 5 654. sino= ]f; "o" o = t.,ii - "i,," o; cos,x=- f , -J sino=tJr-cos"g, "-p= !/r I ;l 105 192 297 = 17.% 17.%= 4%' 9- 6ss. sinP - : .osp Jr sin p: cosp = I l I I I :a.];.:l ::::::i:l .i!!r! ri:,:J "11 1 -"0=1, ,[H 6) 12 12 25 25 ocninb:in ll - Iil"r IV qBepri; , ocEi,lERu c[ &yr I qBepri. 6so. 1! " jn o "oggllg:qqp lt! 8t9. o sin d.os U .os(1sinP ' srnPcosn J2coso -2{si-45'.oso .os45'srns) 2(sin60'cos d rcos60"sinor J3.oso Ji...o z.*.o"o*z 9"i"o - z.f"o"o * z !; "in o - .,.6 "o" o sinctcos0 = "*""."S = '' Jz"oss v2.oso' f sinc J2sino - ". J3 cosd + sinq ../3 cos(x sln d ^ 2sin ocosB - {srne.osll - s;nlJ.osdr - 2sin dcosP sinocosP - "rnpcosct "' costo 0, .os{o + F) sin0cos0 rsin0.os0 sin(d{ 0) -= - .g(d + 0r. cos(cr + lJ) cos(d + P.) OSt. r) "o"o = r.',[ "in'or "o"a= ocKini,Rn Cr - Kyr II qBepri. 9 ./2 i 40 sinrcr 4s")=srnc.os45" rcosl:lsin45' -2 I A) B1E a2 652. cos cr = -o,o; "irts = rn/il "o"'cr; "itt o = .,/i:105f , "i"o = -u/i: o3o = -"6,0n = -0,s. cos(60" - ct) = cos 60" cos o + sin 60'sind = l"o"o, V'"ino= ' t-O,Or !-o t-0,St 0.3-0.4J3. es3. coscr = 9. "i,'o=tJt-*""o;5 sin 0 = s,n,d-Br=q,nn.oqn-.^.^.r"n f t5) 7 ( 8l (-24 ------' t 17) zb t7) zb) "E , s"E 242 40,t8 ^ t e Ee q ^ 34 3 cosl -.Jl - .l : tslj'! 25 25 5 - s5 4 . -'1 3 tgla - g; tgo 190^ 2 .l ^ 5 ,5 = 2. I-tgd{gP I I.J 4 8 24 t2 656. rs{45"+at=-lg1)'-Lgd t 5,1 '-- 1-Lg45"Lga I 12 3 3 3 657. 1) sin 15" = sin(45o - 30o) = sin 45'cos30" cos45'sin30"= ="8 "E _"8 y_"6 _,8 _,16-Jt 2 2 22 4 4 4 z) sinr05" sinr60. 4b"r cos60"sin45.. f 9 t ) " ^tt,3t crp -ro5" I I-=L te60'1s45" r-!6 I €105" 1e(60'r45') rg60'+1945' Jf ' t /r J:)(r Js)_r-?.@-B_4-2$ h, i' ,lltt' "at- t-s -2 ocKi"{blttt cr - kyr III , oclrirbrcn cr x]"r I .rBepri. 398 ii::: AIrEEPA Mep3rcK A. r. ra iH. AKaaeMi,{Hhr pieeBr liii:jlliilli::::i :lit:il:liltii:.rli AITEEPA Mep3neKA. r. ra iH. AKaaeMiqHnn piBeHb al:l 399
  • 658. 1) cos?5" = cos(45o + 30") = cos45ocos30 - sin45'sin30'= J, Js J, y-J6 'E2 22 4' 2) sin75" = sin(45'+ 30") = sin45"cos30" - cos45'sin30" = ,E h "li r J6 ,'E 2 2 22 4 659, npoBoazMo roro*cEi DeperBopeHss niBoi qacrrl ii orplrMaeMo Bspa3, skni aopiBllloe trpaBiii cacrrlri. sind sin0 sinocosp cosdsinp sin{d-pl . 1) tgo igp=-osd r -;= ""ir"*p - *o-"p' cosa sinB cosocosB- sin0sinc costo 0) 2r cls.r- rsL, -{ - ---:" sins coslJ sin(r.osl, sLnosrnp cos rt cos0 coscsinp cosPsino sin{(r+lll 660' ctgq -"iep= "ino " "i^0 = "1"r"""P = sinc"inp c,(Id(td0 cos d cos r srn o cos o cos, o 661.1) z.-___J t z=___t - r=- cts _; I 0 I ct ..r _4 --"4 4 4 .'r cos cr oos2ct _ sin2dcoso co62dsina - sin(2cr-a) - -sind _' sinn sin2a sindsin2ci sinosin2d sinosin2d ^. I 1 cos0cos2a cosdcos2o tt ;, {gf,n ro = -",}*+q re''n d "l"ry = c"",rr' - d, = "."4 = ' cosccos2c cosci cos2d rr is1-:sg lci-lcP -2f,cL-' t-rsdrgF+r-Lgdrgp+2Ls,cL'tgd + tg0 iga - tgF 1-tC"teB 1-te"teP = 2 + 2ts2 ct = 2(1+ te' "l = Z. ]-= ]-. cos- ct cost ct ' 064. 1)cos(o+F)cos(s p)=(cosC[cosB sin s sin Bxcos q cos p+sincrsinB)= ' cos' ct cos'? B - sin'2 ltr sin: p = cos' o(1 - sin'z B) sin'z P(1 cos? cr) = = cos'?cr - cos'o sin'z0 sin? p + sin'B cos'?o = cos':o sin'?p; 2) is(cr + pxl - tc q tc p) (req+rep)=l+l++ 1-tgCltgp (req+teB)= I tgorgll r rg0 te! tgd 1gP 0. r -/t 665. lr s:no Jacosa zlrsina 'i -s".J zrsi""*"60' cosqsin60') = 2sin ({x 60"); 1 <sin(s-60")<1; 2<2sin(ci 60")<2. Hdn6inbrueJna,reHnfl 2- lt; 6 2) sino. cosc Jz """ina-Y-"" - J2(sinocos45'+rosasin4s')= 2 2 ) = J2 sin(0 + 45"); -1 < sin(o + 45') < 1; -'E < .,8 sin(o + 45") < '6. Haii6i,rrue sga.regrlg - .,6. (t" , 666. I I J3 cosd - sin cr = zl vrf cos" - ;"* d] = 2i.os30'cosn - sin30" sin dr = = 2cos (30' + (x); -1 < cos(30'+ cr) < 1; -2 < 2cos(30" + cr) < 2. HanMer ne sEa'reslls - -2. 2) rE sin o + '6cos cr = rO[]"t.". f *""J = = 2E(cos 60" sin d + sin 60" cos o) = 2Asin(o + 60'); 1< sin(d + 60') s 1; -2nE s 2,t0, si]lL((t + 60' <28. HanMen e sga.{egng - -2!6. 667. ItorfteH.IneE apr.OMer*r.rHoi rporyecii, rorrrEaroqn 3 apyroro, € cepeAHiM apso- MerII'rEr{M cyciAHix qnesiB. t4x+5t-lx-+2t , -( Kia{eMo prBHsHHs: 2- - lx - L Z, 4x 5 x" -2=l4x- 2;x'?-10x+9=0; lx. rr"-10. I .r. =9;.r"= 1. r,+j2=91 1. r,=9;4 9+5=41; 7.g l=62tg' + 2=83, 2. =1t4 1+5=9; 7.I 1-6;7'+2=8. Bidno?iob: 41, 62, 83; 9, 6, 3. i:iilitiitili_iati AITEEPA Mep3reKA. r. ra iI{. AKaAeMiqHlri piBeHb iiil 4Ol 1 sin 2cr ' cos 2.r sin2d cosc, slntt sind sin cr cos 2o - cos s sin 2o sinl.r 2dl sin( ([) cosrrsin.I cos ct sin cr cos crsind coscr cin 2d qin o 662. 1l cos2d + = 1 cos(] cos 2ct cosC[ + sin 2 sin ct sin 4.x cos 2cr 2) cos4.I ' 1 sin2c sin( 20J sin 2d sin2& sinz(l cos 4C[ sin 2c - sin 4cr cos 20 663. 1)(sinCrcos P+ cos &sin Bxsin ocos B cos osin B)= = sin, ncos,0 cos, o sinr p=sin'c(1 - sin'z p)-sin'p(1 sin'zC[)= = sinl cr - sin'zcr sin' 0 - sin' P + sin' p sin'? d = sin: o - sin'zP; 2) sin' c[ - 2sin q sin P + sin'z 0 + cos'z cr + 2cos cr cos I + cos' - 2 = = (sin'cr+ cos'2d )+ 2(cos C[cos 0 silra sin p)+ (sin'll + cos'p) - 2= = 2 + 2cos(ct + p) - 2 = 2cos(0 + B); ^ LEr(t ls29 (r'eo-tgoxtgo rtgp) rgo tgp tgo rtgp "' 1 r,e'aue'0 (l rgargBXI rl,gorgp) l rigctg0 r tectgp = tc(o + P)tc(ct - B); 4oo ii:: AITEEPA MepsrrKA. r. ra ifl. aKaaeMi{Hrr pieexu fillllltlli!!::j sin2c, sin(2d 4d), sin2q : i
  • { 668. ItBaapar qreHa reoMerprqEoi nporpecii, roqlIsaloqlr 3 apyroro, € ao6vrlcoM aBox cvciAEix qresiB. CxnaAaeMo piBEsHns: (r- 1X* + 7r=(t 2x'; x2 +7)t r 7 =l- 4t+ 4r'; i - 4tz+6x+ 4x-7 -l=Oi 3x,+ 10r-8=0; D=100 -4. (-3) . ( 8)-ai "lD = z: -10+2 8 4 -1O-2t- -2. ' 2{3) 6 3 2l3'J " a.!-t=!' r z4=-2.! z 25, -' s'3 ' 3' - 3 3'3 3' ,, = 2:2 - 1=lt 1 2'1=-3: 2 + 7 =9. - 1 5 25 - ^^utdno6tdb: .li al -. t:-t: v. 669. Hexan reprEa rpy6a Moxce EatroBHgrn 6aceiE 3a J' roA., a apyra - 3a I ro.r. 3a oagy roarHy nepna rpy6a EaroBHIoe 1 qacrrtrry oacen aa, a.qpyna rpvoa 1 "t"TY rnny 6aceiua. ABi rpy6r HanoBslororb 6acenr ra ? roa. 12 xB. = z* = z ! *u. 605 .IlBi 1p)6 3a I loauHy HanoBHlo]orb ,'r = fi o"""ti"u. 5 c(rraaaeMo trepue piBrr'IrHs 'rcreMlr: 1.1 = :.x!36 IlepIlra rpy6a nparloBara 8 + 4 = 12 roAlrrr i 1? 6ace;ara, a ,qpvra rpvoa 4x rpaqmBana 4 roAlrstl i rlarloBErna i 6aceiiEa. PasoM BoHa HanoBHnrb Becr,6aceirH ! c*nanaeMo apy.e piB'slr,,n clrcreMrl: 13 t ! = t. I 5 |4 4 U'oI I |t-4t. I lir r 36 ) r u e 9 a," re_ 112 4 1124, rgl-+ =I: l-+-=l: I' c l* c 11515113 | =-: u=12.18a 36 y 36 18 I36 BiAnosiAb: 18 !or..i 12 to4. 673. 1) tg 124" = ts(90" + 34') = cte 34"; 2) sin(-305') = -sin 305' = sin(270' + 35") = -(-cos 35') = cos 35'; - tr I n) 3) .rs{-0.?n) = - cue0,?r cr,el 'l r '-l - -1 2 s) [ ''5, -"5' 14r! I n)4l srn =srn fl--l=srn-.15 15/ t5 674. l) .os225" = cos{180" , 45") cos45" '; . t; 2) sin 240' = sinr180" r60') -sin60"--;: ^ 5r ' snl n J2 rjr cos; - cosfr 4 ) -cos 4' -Tl f a,r) 4n / nl n t 4) cos cosl rr+ 3.r 3 I 3l 3 2 675. 1) tg21O'= ts(180'+ 3o') = ie30'= +; 2) cts 315" = cts(360o 45o) = -ctg 45o = -r, n 3l cosi 150") .os I 50o = cos{ 180" 30") cos30' 'r; 4r sinl 5Jrl -"i.8= -.i"lzn ^l- I "i"nl .i,' n - J3. 3' 3 3,r 3) 3 2 2) -ctg(x tgC[=-1; 4) -= 1; 6) cos {:{ + cos & = 2cos ct. 2)-cosC,+cosC[=0; 3) cos d - cos o + ctg cr c.tgq=0; 4) sin'c,+cos'?c[= 1. 678. 1) 3 ts(180" 45') - 2 . sin(180" - 30') + ts(360' ,60") 2srn(180"+60")= 3ts45"-2sin30'-is60"' 2sin60' 3 r 2 ;-Js++= t;, E ^. sin (360" - 45'.)cost360" 60', tg{360' 45") sin 45" cos600 - tg45o zr stn{ro. + 30"r.osr1S0" - 301 cos30'. (-cos3o', r n' "'( ' nr) , rr3) sinIn. 4.]cosl'r-;l l-tclr 5]J"'*['' rJ n r nr ir o "D r Gt Jo ' 'ts cts l= -'4 6) -3 "3 2 2J 4 srn 20".os tO" - cos 20'sln 10" sinl20'r10') sin30" sin 2l".oE 9'- ros 21" sin 9" sin(21' 9") sin30' i:i:iii{iijiliii: alresPA Mep3neK A. r. ra iH. AKaaeMi.{Hlri piBeHb iii:r 403 676. 1)cos (t- cos (I=o; 3)-sind sind= sin'd; 5)cos'?lt+sin?ct=1; 677- 1 cLg a- ctg d= 2cte si L OopMyn]a 3BeAeHHg 670. 1) cos ct; 3) sin d; 5) cos(182" - cr) = cos a; 7) lg dr 9) cos a. 671. 1) sin c; 3) -cos C[; 5) sin Cr; 2) ctg d; 4) cos (270" cr) = -sin q; 6) cos q; 8) -sin 0; 2) te si 4) cte (270' - cr) = te d; 6) cos q. l@l'1., 2)2 1.2s 4 s. - - ;- ----=- - ;'J3 | n3 l 2l z) 672. 1) cos 123" = eos(90' + 33') = sin 33"; 2) sin 216'= sin(180" + 360) = -sin 36"; 3) cos(-218') = cos 218'= cos(180" + 38") = cos 38"; 5n /n nl ,r 4l cos =cosl -+ l=-srn-.' 0 2 181 1a 402 iii: ATTEEPA MepenrrA. f. ra ir. AKaaeMi.rHr4i piBer" liilitlil:l:i::ii
  • d ., cos66"cos6"+sin6'sin66" cos(66' 6") cos60" "' """65'-."5"-l,tr5'"1r65" = ""qAt'-S"l = cos60" '' 679. 1) 4cos(180'+ 45") - 6cos(90'+ 30") + 3cte(360" 60") + tec80. + 60.) = =-4cos45"r6cos30" 3cr.s60.+ tg60.. -4 f 'u I t 4-.n= = z"E+z-"ls+"8=a-z"E; 6111 .,6 6cos'60"ctg30" 12) cos30" J3 i 082, 1) ctg 55'; ctg 65" ctg 75'; ctg 85" saMiEnMo raEreHcoM sa ibopMynorc .rg (r tg(90' a). oAeprRrMo: ctg 5' . ctg 15" . ctg 25' ctg 35' cte 45' ' tg 35' tg 25' tg 15' . tg 5". C$opncralmrcE OopMynoro tg cr ctg s = 1, orpr.rMa€Mo ctg 45'= 1. 2) TaHrencr ryrrx KyriB saMiHro€Mo Ea raHreEc rocrpnx EyriB sa OopMynob tg (180" q) = tg (t. te 20" + tg 40'+ tg 60" + ... tg 60' tg 40' tg 20" + tg 180'= 0. 3) CBopnc?a€Mocr lbopMyrrolo sin(360' d) = sin o. sin 359'= -sin 1"1 sir 0' + sir 1' + sin 2' + ... sin 2' Bin 1' + Ein 360" = O. 683. 1) ts 10" ts 20" ts 30" . ... . cts 30' cts 20" cts 10" = 1; 2) ctg 15'+ ctg 30" + ... + ctg 90" + ... ctg 30" ctg 15" = 0. oea.rrlLeln'Il "rs"l ,loel z' 'l "ig"l -,'.4)")"|41.) | "is I - "ts"J * l"rsI -.is"J = {1 + ctgct'? - 11 - cr,gcrJ'? = = 1+ 2ctgd + crg's + 1- 2ctgcr + ctg'cr = -f - # = #t ,l ft i+(I ,, '"' t " '-"i,.1r..,1."1,,[r -1"-"t] = ,( " (" )l 13 ' -t2 '6 r/ .tq'l d I "2 r6 1) l:t I "ln l /n I - : l srn-L +nl ctg- +{11= .ln I 13 I -3 ) 6cos'?(180'+ 60")ctg(l80" + 3o') 2' -sir(270'+ 30") (-1)' ar "i"fzn - r'J-"1' - n l,'l n,nl".nl 4) 3./ 3/ -tr'6.] =-srn4 l-'os3.]te3 cte6 Jzlt n e ali 2 2) 4 4') cos64'cos4' sin4"sin640 cos(64o-4') cos68' _ cos68" _ _l cos71"cos41' sin41'sin71" cos(41'+ 71") cos112" -cos68" 680. t, -"ino "o"o--= "]no "oto --"o"o' -tgd (-cosd) sln0 cosq coso I sin F sin p - cos B. (-cos P) = sin, B + cos, p = 1; . ( sina coscrl coscrsrndrrgc ' crg0)= cosd srn dl- "o * ",rolsin?a+cosra = coscsin d -=1; cosc,sinc, at -sint"-atslnl " al. sin'rn-atsin2ln+at cos'?rn '"r."*'llI-"I=2 2 ) 2 ) = -cosocosd sin2 nsin'n - cosz crsin'cr = -cos'd sint s sin'ocos'c = = - cos' c( - sin'g o(sin' n + cos' c() = - cos' o - sin'z c{ = - (cos' .[ + sin': q) = 1; 5 sit" t + tg' r. clg', + cos r cos, = sin2 r + cos' r + tg,.r. ctg, n = 1 + 1 = 2; 6) (cos t + sin.r)'+ ( sin., + cos r)2 = cos': r + 2 cos r sinr+ sin', + cosz.x - - 2 cos r sin r + sin'9 r = 1 + 1 = 2: ". tga ( cosx) ,. ' cosr {-igr) -' ^ cos' .r sin'.r sin'r sin rdt - + " .:_+-t_ _ sin..jr rcos"-r I. ctg'x tg'.r I sin'r I cos'"r 681. t) stn qigla = -!!!a . sina coss; teo ( sin0) 1 cosd 2) sin r.sin jr + cos r. (-cos r) = sin2 r cos2 r = -(sin, r + cos, r) = -1; ^. -tgd (-cGd)ctes tgd cosd crgd "' "."a (- rgox cteol = "o"o lgc cugc 'l 4r sinq crso-coso-"'"* -"'it "11", I cosq+ sino= ' cos9 I sinq I sinq = si g' cts cr (-sinel cosd ctgd ( cosq) sin d ctsd(t) - - -Lga=Lgo- l ted l. - cos ct ctg ct 4o4 l{t AITEEPA Mep3rrKA. r. ra iH. A(a,qeMieHrr piEeHr iillt::i:itiii:l """,1r ' ") ".",f' ' "l .i",f" , "lL3 1 "(n ) lsin' + cr L 3 l =.i",1 I *"1 **",1 1* "l = r, .3 / t3 ) 2 3) 3 ) 3 ) sint ct - sin' o(l t cos': o; sint o sin'? o sin'? o cos' a -sin'zcr(l- sin'?Cr) - sin'crcos's - sin' c[ cos' cr - sin2 o cos' o I cos'za I ". _ ctg.11. 2sin'ocos'd 2 sin'0 2 .ln lrn 685- eos"' ' .""'-' ' "".'l " - " l* """' '- - = 8 lt 2 a) !2 11,/ cos'", slnt " r cos' '" - sin'? "' = 1 - t = 2. 8 8 11 3) sin. crl;;5,g I = ;r;: G;;.d) = "t".t-1-."", crxl +;tcr) = 11 ::iltlliillltji:ia AITEEPA Mep3neK A. r. ra iH. AKaaeMi,{Hri piBeHb t::::: 4o5
  • t. l. l. 6a6. t.y cos'1" rol rsin' 'l l'l "l r( sjnsr.coss.iso4 t 2 4 t) .(n ) . "ln ) sinscoscr sinq - =cos'lz+dj+sin'la-".1- I """"=r-srn'd=cos'c: 2) sin':lgo-- t20" - d)) clg (90" (q , tu ,rctg {8u cr) srn'f/u- + 0) - sin:170" Fd' +cLs{so.-rr}cls(8o"-crr=r-crs'r8o'-.rr= ---Lsin {70'+ d, sin (80" 0) 1 = ;JGo% cr) BnpaBx arc noBTopeHHs 6g7,1) ! lo zs; t' 'o-8.0, -rr 3r Io -o txt .r'- 3:c - 10 = 0; = 5, 12= -2. SaMiEro€Mo EepiBdicfi, piBHocr.nr,Horo cncreMoro: lrx-5rrr+2r>o. x(x- 5Xx- 2)=0: r,=0: x,= 5t xx= 2. r.r0; BilnosiAb: | 2; 0) u t5; +-). 2l* -:- 6..0 r'+r--6-0:x rx tii 0ir.r=-J: rr=2.' r-2 t-2 v-2 SaMiHroeMo HepiBHicrb piBllocrrrbHoro crcreMoro: )x + 3x - 2)tx - 2t. 0. Irr-3xx -2r' - 0. lir 2,0r i 2/ol (.r 3X-r 2)' 0r x, 3i.r2 2. BianBiAb: | 3; 2) w (2t +-). 3) r:- 3r- 4 = O, tt= 4i x2= -1. 2x' - x - 3 = O: D = 1 + 4' 2' B = 25' 1+5 3 1 5 BaMiFlo€Mo HepiBHicrr, piBEocun6Hoo clcreMoro: 1 689. 3!(x + 12) r' + 12r. - 45 = O, t, = -I5 se sa,qoBo,rLHs€ yMoBy sa.qaqi; r, = 3. Orrrie, nBrrAKicrb nnora 3 nM/roA. BiAnoeiAb: 3 t<M/roa. g. OopMynra noABiiHoro apryMeHry t flrir ? tra 5 ro,q. 2 xs. = = s| ".r. oi"'**.a 20 xM tIoB€H sa 12 nMhoa. 6in6ua ? 20 RM Hexafi rnBsArcicrE nnora - r I{M/roA., roAi BrAllicrr,.roBHa (n + 12) nM/ro,q. ,n I]nir noAonas 20 xM ra ; roA., a soscH oa '"r2 'o4rH. n,Iir 6yB y nopo3i t20 20 -1 16 ", L _ I t2J roa. b'nhlxe. Do 3a yMoBoro aoprBH$c b roa, -,o4. 20 20 t6 5 5 4 (-xnaAa.Mo piBEflEHfl: ; - ,- n- :t .4i , , , .12 3i 15r. + la} l't - 4r' - 48j. = 0, I 4'' 4sx + 18o = 0l: (-4), l3.r(r+12)*0; 34 t lr,* ou*. rxr ;xr-r,.0. 2r,r-ar(r-;Jr'-rr'so. l 1,, !u' " , o, L.. i,",' Bianosidb: (!: 4 . 12 -l B) cos, a sin, d sin2 d = cosr d: 41 ?!1l25""o"25' "tn rr", 2aos25" , cos" 22'- sin" 22'a sin'z22" cos' 22' "' "n.'zz7-;*22 - '' - cos'c sintc tcos(}-sinaxcoss rsino) t,t - -=cosa-stnc(; cos0 srno coso - srnd 7) 8) 2 2 sin c, cos cr ;?s. "jts = I cos0 2sinccosct 2' 6ss.rr vr-J2 |t-2.12-l.,l2l =Vr-J2 i/(r-J2) =t/r ' Jz.{lr Jzl = {r -Tz lTj r(.n - t)(o r) = tD l = Vi = r' zt :,lr . z.z.1s. (v:r' .,,/zl dtz v:)' ..,/z V: u{z - Jr . "/z - Jr - = lz - 'axz - "a) =.ln-s=ur=r. 406 r:i::: AnrEEPA MepsneK A. f. ra iH. AKaAeMi.{Hni piBeHb iil:i:li:i!!ii!:i:ll: sindcosd ,2. 'r 2-*i** 5, 2.t"1, 11"""1,-1), 12) 12) 5) 6) +)/-T-V -V- 690. 1r cos'? 9 sin'9: 22 2) 2 sin 1,5{:! cos1,5q; 2ts ! ar --:{,1-tA':' 4) cos'4o sin'z4cq ^. 2 ts3.50 trl-. 1- te' 3,5q 6e2. 1y ?!i19!9!9 = 2"o"o, 691 . 1) 2sin 5cr cos 50; .r-B n-B21 2qin .m : 22 - "a "q3) cos'; - srn'-i n, "".,1,{ -, o.l -",",|.1-rn.),.4 I t4 ) 2t91,5d. 1 ts'1,5q ' 2tg6s 1-i8 6d' sin2ct z) '-"- = tgza; i:iliiiiillllll: UTeSPA Mep3reKA. r. ra iH. AKaaeMiqHri pieexu il:i IOZ
  • 14) 693. 2) 3) 4) 5) 6) 7 10) sin'? I - zsin e cos Q + cos'? Q + 2sin I cos q = sin'? Q + cos' Q = 1; r .o ,") rr) sjn" a .os'7= l.os" 4 -srn'41 cost: 2sindcosc sin2s 1. ^|2t - t-p za.i ' 2 cos2o. 2cos2a 2 - r:lr I .os' I ft - c I - "in' I n olll*"'1" or-"i"'1" oll ='"' ["--14 -) -"'4 ,rl r4 t '4 = cosl; - 2dJ t=sin2nr sint n + 2sindcoscr + cosz ([ 2sincrcosct sin'rr+cos's+2sin'n sin: cr + cos'c( , = -; = li ar I "i" as" = €,24 5) ts330'= te(360" - 30') = -tcao" = -+; 6, 2{r - tg, r s.y 1- z"tezo" zJz. 2te15" te30' . t,t 695. 1) cos45" =;: 2) te150" -tg(180' 30') = tero'= €''T, ^. 6fl 3n r nt n Jz;ll srn" " 8 " 4 " " 4) - 4 2 n' -12"..'a-rl- -"..r - -G.t2)62 oso. "o.o -,/l "in'o: .osc l-163y J0,64 0.8. oc!ri.r6&a o &yr IV.rB€pri. sin 2cr= 2 sinocos s = 2.(-0,6).0,8 = 0,96. lst 2l.c(4-5' d) = !!er90" . 2cr . _].rezo; ' 2(l-LE @5" + dj 2 2 16) 4sin o cos d(cos' o - sin'z o) = 2sin 20 cos 2d = sin 4ct. 1r 2sin40"cos 40" _ 2s.n40". cos40" cos 11C[; cos'2P - sin'2P + sin'20 = cos' 29; sin 40"i cos 204; cos'z3c[ - sin': 3a + 2 sin'3cr = cos'z3Cr + sint 3q = 1; cos'g35'- sin'35" _ (cos35'- sin35')(cos35" + sin35') = cosB5, sin35": cos35" + sin35' cos35" + sin35' OgZ. "in cr = tr,6 - "o"'cr; "in cr = d nyr II qBepri. 10) :sin2 cos20 =:l sln 4ct; 1 2 4 2cin2dcos2d 11) (sin'o cos'? crXsint o cos'?rl) 1","f1 ,".] = r"."ro. 2sin 2.! cos 2.r =-=r<in2d.coR 2.r .1 (cos'(p - a5")) sin'(B - a5")) = cos(28 - e0") = cos(e0'- 2B) = -sin 2B; asin ! cos I Gcoscr) = 2 sin d.(- cos o) = sin 2d; .-. 2sin l,scr.f, sin l,5a 2sin 1.5c. cos'1.5{r I sin'1.5s tbl-:tl+-=-' "' cos I.Sa I cos' t.lc , .os 1.5cr cos' l,sa = zsin 1,5<rcos r,5a = sin 3ct. 694. 1) sin 150" = sin(180' so') = sin aO" = j; L zl co" 30. = #: 3, "o"1= J3,'62 4o8 i::l: AJITEEPA Mep3reKA. r. ra iH. A(aaeMi'{Hnr piBexr liiljiii}.i:.:::ili:,i sin 2a = 2 sin c cos cr - 212.( 5- t2o . r3 r3l 169 698. sin? o I cos qi sin'o , U' ;, cos 2s cos? o sin'z oi i1l' 8 1 8 ? .coszcr = I -l3l I I I I 699.cos,cr= r -"i",4: c"s'c,=r l-r' I ri ;/ =1 16=16' , 15 r l'1 15 I 14 coszd cos- 0 .srn" c _ 16 4.r 16 16 16 7oo, Ls2ct - 2lgcr - 2 4- - I -8 . " l-Lg'd l-4' -15 15 ,1 l4 I ll , 2) 2";n9 "6=9 2 si19 8) ' '= '=ta-; 2"".'9 z"os9 z 22 1+ sin 2ct sin' cr + 2 sin cr cos cr + cos2 cr e) 1+ sin 2q ,. 1-.i. r" ' 12, 13) 14) I zot. tgn = -l; tgc'= j. 1 2 si.n' 2ai I 702. Cnoprrcra€Mocfl abopMyraMn 1+ cos2o = 2cos" f,; 1- cosza = 2su."I 2) 2c'ltl 3) 2 sin'z 25'; 4) cos'z d + 2 sin c{ co6 d + sin'z d = (cos d + sin o),. lt:lt{tiiiliilr: MTEEPA Mep3re( A. r, ra iH. A(a,qeMirHrt piBexb tit 4o9
  • 703. 1) 2 2 cos' 60. 3) 2 cos' 2o'l o cr d r c/ 0l4l cos" Zsln cos r sln' = cos- - srn I 4 2 2 4 ! 2 2J 3) 4 6) /.'a ""sa) rcos fl, cos'zdr'sincrcoso . sinzd - - =2i coso srn ct / cosd srnc 1+ tg 1 + tgs 2tlo ,-r-. {1 tsq,(1+tsa) 1 ts:d -"--' - 4Lgotl lg':fl) - sina cos2d sin':d / I " COS O cOS' C' l"*61 = 4 sin o . cos c[(cos2 {I sin' q) = 2 sin 2q cos 2q = sin 4d; sin20sino l'sin2a sincl sin2(lsina sin 2d cos a - sin a cos 2C! cos20coso Icos2o cosoJ .os2acoso cos20eosd sin2dsind cos2dcosCt = srn zc[ cos2dcosd sin(2c - (}) z.:"'!9,12 zo4. 1) Lg19s; - 1 coslox 2. t+"o"1 3. 2' 1+ cos(8x + 20') . 2' 705, 2) 3) 4) 2) 3) 2' 1 cos(4iu - 30'). 2' r'. ii::::iif.:il :i.l;:iiis i!:d.::i.fl 2 sin' 9 2 2sin'9 2 {sin'z a - cos'9 crXsin'? n + cos' a) sin? cr - cos'cr + cos' n 2sin' cr 7) a sin'geos: q = - - =2(os',r r.i"'9 2 2 2 sin' 9 2706. 1) 2sin'zo + cos':C[ - sin2 o = sin'o + cos2 cr = 1; cos3d 2-in'?3a 2l - --- 2 sin 3o.os 3c _ sin 6di sin30 1 .. I {cos i:, sinr o) I cos'c + sin':c sin^ d + sin'o zsin':o "."' "it " ' sin cr sin'q -- "itl" _ 2 sin' 20 4 - = ts'2c1. 2aos'2a 7O7. 1 1 cos(21o" 2.x) sin 2cI = 1 + sin 2C[ - sin 2cr = 1; 1 + cos' 4cl sin'2 4o cost 4cr + cost 4cr zcos" 4d sin2dcos2c[ ', ,""(; il ;r)-"tl'!l ,",.11 ;r-.f 1,;t "''l; "l -." cos 6.I eos 2.l + sin 6.l sin 2cr cos(6cr 2([) sin2c[ cos 2d 2cos4cl 2.os4d. 711- 1) 2 sin 2cr cos 2C[ sin 4c[ = 2ctg 4di 2cos20 2coE2d 2cos2d sinacosd 2l -= s)n Zoi .os c( srn d cos" a sin' 0 -t cos 2d sinq cosd sin scoss 3, t9a__- L€?c-,tga- lg'ct ,21g.! Lg2o:' (l+tgdxl-tga) l-€a cos cr sincrcosfl rcose rsinocoso 2sinocoso 2coso 2sindcoso (1 sin0)(1 sin 0) I I sinT o 4sin d cos'?d =_=4srn(I; /cosa cos2c cosasin2d - sinacos20 5l I I srnzcr = sind Ein2d, sindsin2d I _ sint2o o).fin2& _ sin0sin20 _ I. sir(rsin2(r sin(lsin2cr cos'? c - sin^ c + I - cos' n 1 sin (I cos'o coso 1 6) =--=--ctgcr.' -siD2cl -2sinocoso zsinqcoso 2sino 2 zr2. t cos'( n, ln zoll -"'ln-ln*zoll "o""Ir-zc'I-"o" lr+zaI' 4 ,.1 t4 ') '4 ' a t """,1n zol ",,,]..^ -lt*r"rJ ="". l r - zo t - "r. , r - zo l =t4 , 2 ,4 ', 14 ' t4 /- =.""1 1- arr I = "in acr, 2 ) ;J::t{ilttii{i AITEEPA Mep3rrK A. r. ra iH. AKaaeMiqHrt piBeHb ::::i: 41 1 2sin4(tcos4c[ 2sin40cos4(x 2 sin 4c, cos 4c[ 7O8, cos a = 709. sin d = - "Ez,E utJ,u,d 2222 cl' 5) 4 3' sin2c[ *^ *4?,(;) # 24 sin30cos(r cos3d sin (I sin(3a-cr) _ sin 2cr 7 2sin d cosc ..71fJ.1' srn C[ cos c[ s1n g cos cr 2"i. d ... d 2) _=_ tsdi,,d ,d I -l ^dl 2eosd 2 srn' 2l cos' sin" l 2 2 2 2 2 2) 41o lil: AI|EEPA Mep3rex A. r. ra iH. AKaaeMi,{Hnr piee+ru :i{lil{:iiii{!l*
  • TI 2) 1+ 2cos 2C[ + cos'z2o.- Ein'2.,=(1- siil'z2d) + 2cos 2s + coEz 2a= = cos'z 2q + cos2 2a + 2cos 2c, = 2cos2 2c[ + 2cos 2ct = 2cos 2s.1 + cos 20) = = zcos 2a . 2cos' d = 4cos2 d cos 2cr; 2srn2 2d zcos'2d 2sin' 2q 2cos' 2(t "' I I I tg'2ct ctg'1 2ct cos'2d sin' 20 2sin'92c[ cos'2q 2cos2 2d sin2 2d 2('os'20 sin? 2cr) = 2i 1 sin'2c 1 cos" 2d 1 r sin2c-{cos'o sin ct) 2sin':a+2sins.osct 2sjno(sino-cosd) t'l*"in2ct*("*'o"in'o1=z"oJo-xino"*o2-"o"ot"ino*.o.ol sin'? Cl - 4(1 sin'?ct) sin? 2cr - 4 cos'z ct 4sin2 o cos'? c - 4 cos? cr = z"in"z., g"into ' s"in'o-" o g"in',* = I Ssin'.[ cos'2cr + sin'za -.- sin?5" ros?5' sin'/?5' cos/ 75" -2cost50. -cos150, cos?5' sin75' cos75'sin75" 2cos75"sin75' sin150" = 2ts15o' = -2. ts(180' 30) = 2ts30" = 2J3. 1 716, cosd - sin o :, ni,aHeceMo o6rABi qa.rrHH 40 nBa4para: :t sin'za-2sindcosc ' "."' " = l, I I -sinzo 1: sin2c=1-tr sin2o q 999 717. cosg-sino l, "o"'9-2"o"9"ind ' "in'a "1, l-"ina 1, 2 2 2 2 2 2 2 4 4' "i,'o = r 1' "t.'o=9.44 218. tr 2sin r 2sinocosa _ 2"in{l*"o"q] = "ino,zcosa+l-1 2(coso rl) 2) cosl q 2sin'scos'?(t+ sinn d 4sin, crcos,o= (cost o sin, cr)! - sin, 2a = = cos? 2cr - sine 2cr = cos 4cr; 714. !r1q * ig:lli = sin'? 15'+ cos' 15' ^. cos 2c cos 2d ot ------ = t : cos cr 2 sin'z .r cos {x =_=_=_=42 cos 15" sh 15' sin30" 0,5 cos 2d. sin 0 cosq(1 2sin'zcr) 5) , 4cos'!d(sin'0 1) _ 4cos'o'( coslcr) cos'c 1 2s1n'n 2 -Ssin'o(cos'z (} - 1) 8sin'ct (-sin'za) /. co.I : - 4d Icos2cr'" lr __ J'_- sin4ocos2d 2sin2dcos2dcos2d 4srnqcoscr "' 2*"' "-%""'2,a acos'qco"'24 - 4cos'crcos'2c 4cos'?c cos'4q cos' 4c cos' 4c " tg2a - crg2rr sin20 cos2a sinr 20 cos'?2q cos 2s sin2c cos2qsin 2c cos'4s 2cos2asjn2ct cos'4d sin40 2cos4ssin4d I -"--:-. '"'--:::r '- -:sinEo. 1 2(cos'z 2d - sin'2d) 1 -2cos4ct -4 4 zr3. rr sin,lz+1" no I I - "in' I " * { I - a") I "i"'[I +"1 - "i"'fI . a"l ='- ,- l',4 r, | '4 t 4 "j,,11 ln noll - "in,l tr +4al= cos,ll *aol "i,''f*lol- 12 {a -') -'-'q ' 4 t t4 l = coslU + acJ = sinsa: 2) 1 - 2 cos 3s + cos'z 3cr - sin' 8ct = cos'? 3s + cost acr 2 cos 3cr = = 2 cosz 3c[ - 2 cos 3(r = 2 cos 3s(cos 3C[ - 1) = 2 cos 3cl(1 cos 3c[) = -2cosBq 2sin,4 = . +sin, Sgcosiro; 22 2cos'2d 2cos'?2c cos^ ct sin? c :{l - - cos0 sind 1 sindcos 0 "it- - "." " 2cos2dsin2a I 22 2 sin d - 2sin acos 0 -- 2sin'9zsrnq(l cos d, , ,2u ,"tr ot1- "." t) = ,"-+ q ='ts t 2 | ''n'2c 41 zsin4d ll-Le'2o)='"'no" l ' ^"-o"'ro'1+ tg' 2d. 1* "i": ?" -. cos'2C[ - sin" 2a cos'z2o, sin'?2o 2sin4.r cos 40 .n.2 2a = zsrrr4d. -^ ^ = sin a.r cos'2c cos'2c cos'20 1 sin'2a+4sin{I][-sin'2d sind 1 4 sinn C[ "' 4(1-sin'3d)-sin':q 4cos2c-4sin'ccos'a 4cos'a(l-4sin,d)- 4sini cr sini q. zl cnq'z o nnc': o cos 2ct cos 20 coE20. "i"11-2'lt2 ) 6) l 2 cosz 2Ct . sin cr cos d cos2c 719. 1) cos 2d sin2 2a cosa o sin'?o I sm_ t[cos".r".".2d f".":d "i'1q I sin- c cos" q/ _ cos 2ct . 4 sin'2 c[ cos'9 s . (cos' s - sin' a)(cos' ct + sin' a) cos2ir 1 _ 1, 1 sin':scos2q 1 Acos2d - 4' l:ifii:llitlil:il AnrEEPA Mep3rsK A. r. ra iH. AxaaeMi{Hri piBeBb i3l: 413 4) 2 sin c, + 2 sin c[ coa a[ 2 cosf 'r - dl "t", f ' "l , """1' - "l "'.l." ")4 / 4 I 4 ) l4 ) (n ""la - "J cos20 4t2 it:: AITEEPA Mep3rrcKA. r. ra ifl. AKaaeMi'{H!,ri piBenb :i{L:{tii:i:;ii
  • a[*",] "'" ;)(*ui''"*']] sin o +sin o r"-'la! +.r" i 4"t" ;1"'"';-r) sin'o 4.4sin ! a"r''!"""'! a[r .r"'!J a-"']1"r"'!-r) .,;i (-s*il =.,"'i,",e, *",; [-*",]J *" I ' 2 5) 2Eir2a '"'"Il ")"""[! G.")]='"'[i-,"""(:-") = "'[;-*) = = '"'-- =::cte2o.. 2si.n2d 2 " ?20.1 8 sin 3cr 721- 1 2sin(30 d) cos2d 1 ^ sin18'cos36'2cos18' 2sin36"cos36" sin72' cos18" 1 4.W - 4'18' 4cosf8" 4' 2n 2n 4i - 4n 4fi 8,7 4 sin Z sln cos _ I I I _9_ I =_ e = --^ 3. I t4cosrr+.oszd-l 4(1 tcoso) {l "o"ro' 8"o"'o -2"in^c 3+1 4cosd+cos2&-1 4(1 - cos ct) - (1 - "o" 2") S"ir,,!_Z"tn,o 41t 4n 8n Zsin sin _ 7 7_ 7_ ,11 1t 1 sin'3ccos" cr cos'? 3c sin': a srn'.lcos- d (sin 3d cos c[ -" sq!]lg)c'" tryg! "l *g:qS!qg) = ,T ,r 2fi 4n lisrn cos cos cos 7777 .n 7 4n 2n 4ft 4sin 2) 7 4sint3s .arsinl3./ rat ,1q1@ !l1o 4sin2d 2sLn2scos2a=8cos2d; sin? 2(} sin'?2a sin 2ct .cl "c ^ cos r/ cosd 2 2 ct t ,u. ao sin cos sln-2-222 ')d rq 22 (n) sm n+- -sin|tt 7__1 .n 7 .n 7 1 22 1,$n u; "d "cL13..s' llsrn' .os" = 2 2 2= ,d - ,c .d asm- asrn- cos' 222 "-.'sfr .r'sl2 2l s.i"'s[ -.'sl = ' '=rt,s'. "d ,d '2 223, ,"o"'o, "=(sin'(r + cos'o)' sina c + 2sin: cr cosz cr + cost a - 1- 2sin'ncos'cr 1" = ... _ = --cts'ct....2 qin' d.os' a 2 "(sin'z u + cos: s) I 2sin'9 a cost cr 724- 1' (Va + al + ({/a b) z:la b '{a + b :la+b-!a-b) . 2sir2.l 2') a) qE-.tE.b ite: ! lr b . 16- lf'+b ' (Va+a-Va-a) 3Ja b 1!o+b _ _,: a lo t to+u tla+b-.9!a+b) = lCn {'4. 2cos18' n2a4T>lsrn cos cos -. q I I I 1l I .( nl z srnl JI -l srn 9.r I .. sinl sin ll 99 2sin3d sin 24(x .71 n srn -99 3) 2sin 3d cos 3c[ cos 6ct cos 12(I 2 sin6qcos6clcosl2c[ 2.sin12cl'cos 12ct 725.12x-a<O: 22r+6>O; 31 0x 2 <o; 4 r+2<O. 726, N 3srai6Ha kirLkicrr, DoAiii. N(.4) - IlinbKicrb EoAifi, sld Ba.AoBonbnsrorb t'MoBy A. N=40. 1) -4 = {noMep KBaprnps, repEe qrc,'lo}; N(1) = 20. prat = I!l:! ",o, = ?9 = !, N402 2) B = lEoMep l(Bapfiipr .rrcro, IiparHe 5); NrBr = 8, Pr-Br 8 l, 405 3) C = iEoMep (Baprr,rpr Ma€ oaHaKoBi qv Oprli NtCt = +: PrCr = -{ = a. 40 lo i:iifliiiii:ilif uresPA Mep3rcK A. r. ra iH. AKaaeMi.rHxt piBeHb i:;i: 415 I 2 2sir''s. 2.4 sin 3cx 2sin54"cos?2"cos54' sin108"cos72' 2aos 54" sin(180'- 72') cos 72" _ 2cos54' 2sill 72" cos72' sin144' sin(180" - 36' 4cos54" 4cos54" 4cos(90'- 36' ar q ;::* utrespa Mep3neK A. r. ra iH. AKa,qeMi,{Hnr pite"o liilllllliill IE-.E+b
  • 2) cos 15" > 0, 15" nyr I qBepri. 728.27O' < zcr < 360', 2ct - lcvr IV'IBepri, cos 2 q > 0 t..; ti ll 1 "o"zo,.,t-"'"'zo-J,-l Y| -J,-; i; ;,Iz sin 0 > 0, C[ xyr II qBepri. 729. 18O' < cl< 27O', d rcvr III'rBepri, cos d < 0' - '... ;, 6' l a 11 1l. vol L o coso -!r Itr -!,a= {r- z. .,I ^ sin; J, l, ,f2 J, z Jzb .Lz) 2J2 2 .-8 r*"."n 2 2t 2 2_J2 12+J2)2_Jz) 2 4 2tJ2 tt G , - 2 -,'-'' 732. o' < c, < 90'; o'< ;<45'; I ." - lJ - Ryr I qBepri. ",.[n'" - il ' o, @" Z) *vrI.rBepri, "'(,r-|)'o' F - """(ro'- ", F -r."(ro" - "),, ! , vl-slng {l+sinq r.u[+ "l" o f r.,/i "l" r f Jt v/i - "ir* f + "ir " ="1-"(;-91-r"*(;-91, n.,.o, "o"ln-9J .,0, r<9<1. ","[l-tl .6. 2 4 2) 4 2 2 4 2) ,[ J2.".1 l-e1- Jz "i"{ r- e]l= 21"i"r"."I 1 ql , -"^"*l ' q tl" 2 4 2t 2 4 2') t 4 4 2t 4 t4 2t) = 2","[l - l - e] = 2"1"(l - e'l = 2"".e. 4 4 2J 4 2) 2 ii ili$illltil AITEEPA MepsrrK A. r. ra iH. A(aaeMiqHrir piBeHb {ll: 417 l4 yci rAB l0M,!. l 3r rs?b"= . sinlso. sinio. r.1, "61 r z 1.(r.,6) " I r.ost5o" t..os3n. 2 | 2t 2 2 J3 (2_J3l(2_J3) =lj="*,0' 4) cos 75" > 0, 75" * xyr I .rBepri. "Ez , Jz tz lz , _ _Jz(z ' _lz = -rQ"." = .{, .r,=-;E-A=-6-1il6;til=- 4 ' '/t+"i"" t Ji-si"s 1 --rffi-_--rffi= l+sincr-l+sin.r 2sin.r Jz Jr sin'c r/2 cosa "o"9.0.2 - Ryr II cBepri. 730. Lc'{T-ol=,u'1"-ll "11,, |;,",'lr=ryj- I 1+ cosl + za) J 2 sr Ls112.so.= _jA??q sin{r80o-4sot -sin45. .E f, Vzl I cos225' I r cos(!80" . 45") 1- cos45' 2 ' - , r,' 8 ,tzn ' : 816 t cos'2c= I-l- 3J =n,rg'1 o -ol ,-, ,;=s's z [ 3// 731. l)sin ls" 0. 15" - I{vr I qBepri. 416 lil MTEEPAMep3ntKA. r. ra iH. AKaaeMiql"r pi"err lliiillililllf::J
  • lr 1O. CyMa i pi3Hxr.lt cr,rHyciB (KocnHyciB) 733. 1) 2cos 35" cos 15'; 2) -2sin scr sin( cr) = 2sin 3c, sin (r; B) 2"i,5P"""f-qll 2"i"5q-"8,2 21 2 2 4) 2sin 1'cos i"; 5n 5n ,'I 5) 2cos cosl = Zcos cos"' ' "72'" 721 - '72" 72' - tx r(I) (r.-d) {r ts) tr -(r) ^6) 2sin --- cos , zsrn.rcosn: _ {a 0t-(a+0, {o ll)-rd+0r ._2srnscos( F)= 2sinocos0:t t -zstn 2- cos - 2 tz. -l-lz. nl r:o-"J '[- ^l e' :.i,f-- !l l !l"o" 6' 3' - 22 zrr-n zo+L 2a-I +z< n ,"r,, -"--o--l 3"o,'* 6-1 3 z,in tr "o"l z,y nl; 2 2 12 14) 1",,1 ln-"r f^ "l " er 2cos J rul ls-urcos,, " _!_"1 z"os1.oso= z.l.o"o-.o"o. 2---232 734. 1) 2sin(-10') sin 26" = 2sin 10" sin 26"; 2) 2sin 20o .os 8': 3) 2cos 4d cos(_Cr) = zcos 4d cos c[; l) 2"n{s'0t-to-0r.osrs 0) r(d-p} 2sinp.qso: 22 l^.1*ln-*l lnrol 'T 5) 2"inl 3 * '-* "o"'3'" --Lol 2sinl"osa-2 f *"o= va, 2-232 . (n , (n ) or z",n[r'"1-lr-i-1".1t "]'Lt-' r",,*.,"i=r.f"'"*= = .,6 sir cr. 735. 11 2sin5acos3d = "in5o = tnbo, 2.os 5.rcos3.[ cos5cr er 2sj n 44'sin 30" -tsJ0.= Jj ' 2sin44'cos30' - 3 236. 1) 2cosSc'cos.} = ig!i!: '2cosSqcos(-4cr) cos 4(x 2sin 2cr cos 30 2l - = cis3cr: 2sin2.rsin3d 2sin6asinr 5al sin6a 2l -= = tgoct: 2sin50 cosOd cos6(l 2 cos 45" cos 13" : _=cts4be=1. 2sin 45'cos13" lc 737. lr sin20'+cos20"=sin20" Isin70"=2sin45'.osl-25') 2 ; cos25' = J: cos25'; zr "o"n -"o"8 = zsinn"inl-11 = , . J' "'n ! - '8 "i' 1 ; a a 4 8/ 2 a u 418 ItJ AITEEPA Mep3ncKa. r. ra iH. AxaaeMi.rHrfi piBess t:iil{ijti;i:i;:l , "-1-o ono,o 3) sind - cosd = sind - ",'l] - "J = z"r"--|--.--f z"intr"."l c.-rl=2.@."..1 "-ll=./2"..1 .,. nr, 44)24,r4,/ 4) sins sin(90" - d + 60:) = sind - sin(120'- cr) = 2snc-120'-dcoso I20" o = 2srn{d - 60"rcosG0" = 2 J"ir,o 66'1= 222 = sin(cr - 60'). 738. l, sin 2s" F sin 3s' - 2sin 30'cosr-s") = 2 ;cos5" = cos5": 2) cos 22" - cos 24'= -2sin(-1") sin 23'= zsin 1" sin 23"; 3r srn.r, sinrgO' or 2 "in o - 90' - o "os o - 90" + d 2sin45"costa-4s"1 22 1r- = 2.=cos(cr 4S') = J2cos(o - 45o). 739. 11 2l | "o.ol zl "o"n-cosdt-2 2 "t,' a ' o "tr' 1---a = 2 ,] t 3 ) 2 2 t; - 1o 1"2t 2 Vr-"."a =zl "". I * "". " I = a "n" 6 "o.62 .r 6 ) 2 2 /n a) /,r crl =4.os -+-,12 2) 12 2) i) J2lJ'-sindJ =J2lsin;-si^ol=J2 2"i"[; ;1""1 ; ;] = z,E.:,(! sl"r,lr.,. sl.' a 2) 8 2/ zm. rr:l 1-"i"al =rr .r"n "r.ol ."r"f ^ "1"."f. ".], 2 ,r 6 ) .12 2) t2 2) ,, rl,6 -"J zl """ tr - """ o I = r "i" I n -9l"i"l I+91' '2 r 6 ' rI2 2' '12 2) ,, rl@--.J=21 .""1 -""1 z zcosl trrol"o"t n ol 2 / 4 ) 8 2/ 8 2l in al fn rr) =4cosl + R 2l la 2l 741' 1) (cos3d cos4d) - (cos5rl - cosorr) = 2sin9sin+ - 2si"*"i" i ='2222 "l 7a ttol 0 9.r 11 9.r = 2sin- sin sin 2in 2sinl f.l.os -4sin .os.222 :a::ii{liiilrii:: A'lTEEPA Mep3rsKA. r. ra iH. AKaAeMieHri piBeHb illi t4* 419
  • r 2) sin 4q + sin 8(r + sin 12o = (sin 4(, + sin 12cr) + sin 8s = 2sin 8o cos 4d + 2sin 4c[ cos 4{[ = 2cos 4d(sin 8c[ + sin 4ct) = 2cos 4d . zsin 6s cos 2c[ = 4cos 2c[ cos 4s sin 60; 3) (cosd -cosp)(coscr+cosB) = 2sin9:!si"";0 2*" "; B-" o; B = 0 n B-d cr+B s+0 2sin ',____: cos L .2sin ' cos _______: = sin(o.p.)sin(p_d): .. 2 sin 2cr cos o - 2 sin 6c[ cos e 2cosd(sin2{+sjn60) _ '' 2cos 2d cos d - 2cos 60 cos s 2coso(cos2c + cos6c) -. 2(sin2d + coszd) 2(sin2o . coe2d) Dt Gos;- cosSc,,)-(sino - sinss) = 2 ";n 2o "in o-lllf,f a) cos 2c - 2(sin 2C[ + cos 2d) _ 1 - 2sina(sin2s + cos2a) sincr' z coJ l ', z *" 51 -" f r*": f""" : "o" tj l r"o" 3j "* o ' ,# i = 2coscr:-' cos cr - cos 2cr u "." 3_ "o"'222 zr +"rn,9:-0"in, Lo ' n "i,', 9:! "o, o ' 0 222'2 _asin.d-Pfsin,s'0n"o",*-0.l =l o B 22L)stnzl sin'd-2sindcoso rcos2s _ l+sin40 sin4a sin2d+1-1 ' 2cos 3.r cos rI 2 cos 3q cos o 2sin dcoE 3ct tp ar: 2.os d cos 3.r 9) sin ncos 2.l - sin2d cos cr -2sin4a sin(-Bq) 2 sin(cr - 2ct).2 sin 40 sin 3cr d-p d 0 q+p ct-p =z"o"L-0 z"in z - -2"".--.r- z 2"..d--q.2"i"9.""0= 222222 fI 0 rl-R = 4sin cos rcos r. 222 4) (sin o sin0)(sind - sin 0t = 2sin a - 0 co" LLq. 2"inan0 "o" o - I '2222 = sin(o + B)sin(a B); . (cosd- cos50) {cos2d-.os4d) 2cos30cos2cr 2cosgdcosa (sino"sin5a)-(sin2ct-sin4d) 2sin 30 cos20 - 2sin 3d cosd 2 cos 3d(cos2ct - cosdl 2sin3ct(cos2d - cos o) 6) sin'z d + 2 sin o sin B + sin'? p + cos? c + 2 cos o cos B + cos' p = = 1 + 1 + 2(co3 q cos B + sin C[ sin P) = 2 + 2 cos(d 0) = 2(1 + cos(d - PD = = z.2.o"" " UF = q"o"" q ,F ; -. sin 2d.os 4q 2cos:c I ' ' ^i. 2o "-* 2 -.4** = t' sin40cosd - cos4C,sind sind + cos30 2 sin4C[ cos2s _ 2. sin3cx .2sin20 cos .x 8) ... sin2s 2sin4d-sin6d {sjn2q tsin6Ct)-2sin4q ' ' ' cos 2c - 2cos 4d + cos 6d (cos 2q cos 6c, - 2 cos 4a _ 2sin 40 cos2d - 2sin40 _ 2sin 4d(co32d - 1) _ ls4fl. 2 cos4q co6 2d - 2 cos 4d 2cos4o(cos2ct-1) _ 742. 1 t 2sinttsc@t 2si" r ;d "." ; = 2*"i ["'. t1" - "'" #J = = z"o"f . zsnlcoso = l-"9"o"o. "i,'?; 2) 2sin2dcos(r-2srnscoso 2cosplsin20 sinar zcosc 2sin]cos3f = ft 3.r = 4 sin tcos0 costi ;rr:"i,9i-0"n"9 P | 2 "i,, d - q "o" g--q - zcosd-pf"i,,g-l-p '"ino 0t-r ;- 420 t::i: anrEEPA Mep3neK A. r. ra iH. aKaaeMi,{Hnr pieexu llilil*{l:Iri*i sinAcrsinc[ 2 sin d cos c[ . sin 3(x sin o 4 sin 2c! cos tt = _ = 4cts.r. sin 2q sin c 74g. 1) It t cosqt . sin o = 2cos 9 - 2"ina "o" I = 2"o"9[-"g..r" *l -' 2 2 2 2t 2 21 =z"o"9l *"9-"*l n -oll. z"o*9 z"o,;'; ;.".;-;.i = - c fi ld nt J2 0 rc rl r.! r,4cos2cos4.os[ ' 7t-e ' cos rcosl2 i)-2.r2cos2-"[t-;], -. 1+.os4d - sin 4q zcos'2.r- 2sin2d.os2d 2cos2d(cos2cl'-sin2ql l - cos40 sin4d 2sin' 2d - 2sin 20 cos2q 2sin2a(sin2d+cos20) =_=cls2ct: sin 2d s) "i"'(?-rd "") **(!-'"-r") = "*.(; - -)- *c(; *)=","(;.^) ="',(:..) ",,(T--)= = l"in I tr rzqt. "ini9r * zo I ll "i"l ft , zol+.i,'1!I*:.'tl=r '8 r 18 t.) 18 I L8 ') =,"*f-;)-"fl.,"l z"r"{i-z"l-"1-lJ "i^}"i"1}.a"J - 1 cos 4.r =-- cos4d = --. :iilll:;:iti:i{i ATfEEPA MepsreK A. r. ra iH. AKaaeMiqHirr piBeHb !t! 421 sin 2C[ . cos 20 sin 4asin d I i I =sin,f-1-2crl -"o",11 ,".] = 8 ,/ 8 ) -"*,ll-ll-r"ll=2 8 t) = 4sin 30; 10) -2sin2d sin( o) . 2 sin 2d cos c[ zsinz 2a = 2sin 0 cos q = sin 2c;
  • 744,l 1+ cos2d-zcosd = 2 cos'z c, - 2cosc[ = -2coscr(1- cosa) = 2cosa 2sin'9 = 4cosasin' 9: 2 2' 2l {.1 - cosa) - sind = 2sin o - 2sin o cos a - z"ir' o l"ir' o - "i"l I - S ll = 2 2 2 2 2 t2 2)) =zsrng.zsrnr g I "..I=4 J2 .r"9"i.19- ar"l= 2 2 4) 4 2 2 2 ) = z-8"i,9"i.[9 - +s"],' 2 2 l :r (-"il-:,1-*"t'; -t)["."tT *] -"rT.*t)- = -zsinf sin(-zcr) zcosf cos(-zcr) = sinlcr z$. (u6ra,-r")'= t'-rf , s + 8x - r, = r, - 6x + st -2x, + -2x(r - 7 = O; xr = 0 a6o r -'I = O; x,= 1. IepeBipria: t. ' or ,,6.4 0 'd o':, r 3, piBHicrh HenpaBx,rbHa. 2. r t, Js,8 7 -7' -7 -3i 4 - 4. prBsrcrb npagunbHa. Bidno6idb:7. lr 3i x, 2. ITpppBipI{a: r. ,,c = :; n[-3y - 1 3y,6 = itt. (':); ."6 = .,6, pinricrr npan,r"rrna. z.t z: Jz z a Jzz: Ja v a. Btspa3r 3riBoro ra flparoro 6oKiB Marorb aMicry, 2 se € RopeseM piBE EEE. BiAno6i0b: -3. B) (.,e+6 .,6 ,r)'=(z 2x'i @+6Xb-2')=4 8x+ 4x,; 5r=2t, + BO -l2x=4- 8t + 4r2:' -612 + r + 26 =0 : (-1)i 6x' - z - 26 = O; D = (-11' - 4. 6. (-26) = 1 + 624 = 625. /n _ o<. -_1r25_26_13. __l 25_, ' 2.6 12 6 2.6 fiepeBipr.a: BiA'eMsoro sfia.reHHs, piBsicrE senpaBr,urEna, 2.x 21 ,[z-a uli.z nzl z z t-ztt BiAnosiAb:2. <,1 /a- r l '' =r"['*t J5,-2, r 31 2 3J(3,r r I r3ir - 2r: Jt' z :,': :n6l r' :,rl ',r ,,6*' r* z: rx-lr'-.(J9,. -3r-2)': f +2r+1=9x'_3t- 2;8x'- 5r-3=0| D=( 5' 4.8. ( 3)= 121; 5+ll 5-11 3 JD TIi .X L X" 2.4 ' 2A 8 422 '.:., AII|EEPA Mep3nrK A. r. ra iH. AKaAeMi'.rHr4i piBer" i:ii;ii:i:iiji::l:* srn1a = sin4asrna = sin4a. 22 14x - Ot Brpas ia nparoro 6oky Ea6yBae 13 6 IIe € IcopeIIeM prB]rnr r.fi. 2.3-6;6=6. IlepeBipna: 1.,r l; - rJ3 l-l=3,,i3 1+l; J3.1 1 .3B'pas He Ma€ sMicry, -; He e RopelreM piBEsHEs. BiAnoqiAb: I F I;; t- r- z+a. -s,[z -a,.,!z'.2 ap]' 2"1'' {2 s .s.E + s,E + eJ9 - 6:14 - 26 = v9 !4 27 2'. . z"Jz t a.lz - z{s t t""z - 2""6 = etE. 747. Hexaii ro.rarnoBa BlrAtiicrE BerocrtreAr-rcra craEoBnna r KMhoA. Ilicnn B6in6- IneHEs uBr.rARocri Ha 30 % Bo1la crasoBtlrL 130 %, rqo AopiBEIo€ 1,3n KM/roA. nicns sMeIImeEIIn rrB*r,ariocri Ea 20 % BoHa craEoBrrb 80 %, rlo AopiBHro€ 0,8 (1,3r) nM/roa. = 1,04r RMlroa. HoBa rrBraRicrE 6irblfle Bia noqarrcoBoi :da.1.O4x x = O,O4 r nM/roa., rqo craHoBnrB 4 % BiA ro.rarlroBoi flBnArlocri. BiAnogiAb: 4 Y.. I 1 . OopMynn neperBopeHHq Ao6yrKy rpnrououerirvxnx OyHkqifi y cyMy 1) ;(cos(15" 5") + cos(15" + 5')) - ;(cos10'+ cos20'); I 2 ; hos(3d - 2c) - ros(3a r 2ci)) coso r cossar z |tcos((cr + ts) (q P)) + cos((d + P)+ (o - 9))) = cos29 + cos2a; t( ,n rr ',) 3,r 5'r 3n 2 sinL --l-slnl -r- l-sin lsrn sitr 2( lr0 40.1 10 40.,1 40 40 40 8 jt"t"tup - nol * "rnfup + ao))= ]lsinza + sinroal; lrcosr48" ?4") cobr48'.?4"tr - 1cos26'-fcos122"=lcos26' lcosr8': 22222 z. jf"*fo - zol - *"(([ + 2o)) = cos cr cosSd' 2 ;(cos((60'+ d) (60'- d)) + cos((60'+ o) + (60'- cr)) = 6=6. l il I I ....1.:.:nL::. l::::i::ll ,ri*tf::::aa.!:{ iil:illiil :fq i I 748. 2 3) 4 5) 6) 7 8) |"o"zo I "o"-tzo'= lcos2o ' lcos60" = lcos2o ' l. 22222 ron.r' l.rl"""l r nl,"o.l n,nll ""'l - 3n l - "." 1sI - "o" 33 * "o" lq 2 t '8 5'j '8 5') I 40' 40 40 40 z);cin(2s' 24') sin(28" + 24')) = lsin 4'+ l sin 52'; 3) ; kos(5d - 3rr) cos(5o + 3a)) = j cos 2o - j """ ao, ::::;t:::gil{l!: AIrEEPA Mep3nqKA. f. ra iH. AkaAeMi.rHrn piBeHb t:i:! 423
  • I 750, 1) 2. ; (cos 20" + cos 60') - cos 20' = cos 2g' t ! - "o" zo' = !; 2) sino + zsinocosd = sl"a + z. jGint lx) + sin gc{) = sinc[ sinct + sinSq = = sin 3c[; 3) 2 jtcoso + cosao) cos 3cr = cos cr + cos 3cr - cos 3d = cos d; +l cosza + z f,rcoallr-+ 30') (d - 3o')) - cos((q + 30") - (c[ - 3o'))) = = cos2q + cos60o coszcr = "o"60'= ]. 751. 2) z sz. U f, coaza - f; co" ao * j "o" ao - j "os 12cr = ] (cos 2a - cos 1 2o) = ]t-z) sin zo slnt-sdl = sin?c/ sin sdi ,, I [","11 r - ro I I o * zo I I - "i. i I n * so I * I * . zo I I | --'2f' ll4 ---t t4 rl ll4 t 4 ttl r[-"llr-*] ln-ooll "o.[ln*ol-l'l eolll = 2[---la ''r'a r] L4 ) t4 t)l =11 "i,,so,"r.'l I+zol "o" zo * "o"ln - so ll = 2f-----' 2 t t2 tt I - - -l z "inno"osd = sin4s'osd..- 2 (sin ird - cos 7ct - cos /cl lsrnbdl 2 753. 1) ; (cossct + cos 9cr) - j (cos 3o + cos rrcrl = = |{cosScr + "o"so cos 3cr + cos r ro) = } (cos 9o cos11d) = = ] t-z) "t,,{-o) "ln roo = sincrsinlocr. 2) BnRo1raeMo roro)r(Ei reperBopellss niBoi i rpaBoi 'racrrs: r. z"o"a I snlld+rs"l-ld rb"ll*"inll"-rs.l-lg rrlll=-2 2l--tt 4 ) t4 )t t'4 t 4 ,l r( a t d 0 d = cos ;lsin30' sin ;J = tcos 2 rcostsin 2 t 424 ;.!* ArlfEEPAMep3rqK A. r. ra iH. AKaaeMiqHnfi piBeHb ititilliiil:::::: z. 1l"nlt+s", dl las' 33ll . "'"lr ar" * " J * I ar" 3"tll .- 2l Lr 4r | 4)t ,' '" +'t) 1 lf^^^dlt lotc crd = srnd+ 8rn 9U" | - sin(1 r-cos-= -cos Tsin cos.. 2 2 2) 2 2 2 2 2 2 2 y peBynbrari oAepxyeMo piBEi Bnpa3r, B ,IlBii i rpaBii qacrrEax. 7sa. 1r sin d+1lco"lIn-ol I^, * tI * "..1 I r - "1 .l 3 -"1ll2l Lr3 ',13 'r r'3 "3 tl) sin'o r I cosr 2.,, , 1"".4 = "i"'o * 1"."2o * 1l "." *l -2 2 3 2 2 3l t " I . 111 11r rlslr'(I l-cos'd--sr["c+ lcos" d lsin'.I1- -=---= : 2 2 22 2 4 2 4 4 zt cos'o -cos'0-1rcos(cr-p)-td- p)t cost(o p) | (o -p))= -- cos'o , cos'g -|rcos2p-cos2dr cos'o rcos'p j"." "-i"'"'U- -]-" " - |"r"'o l*"'' j"i^'0 , I "o"'o - 1"in'p = = ]r"*' " + "i"' "t* ]1"o"'9 + sin' py = 1 -r 1 = 1 3) cos'(45"+o)-cos'(S01-o)+;(cos(15' (75" 2q)) ' cos(15" + (?5. - 2d))) = =coF'(45"+d) cos'(30" - d) +;cos(2cr - 60') - jcos(9o" 2o)= - jtr --"rso'" ,"rl )t '.osr60' - 2cr) - | rr + cos(60" 2a)) Isjn2d= = i-!"^^ -i -i"os(60" - 2cr) +]cos(60' -2cr) - 1sin2cr = -sir2q. 755. 1) ;G - cos2a) + ]0 - "osz0l + jtcosrta + P) - (d - p)) + cos(d + 0) + (e B))) = I l"o"zo,l-1"."24*1-.20+rcos2n t: 22 22 2 2 z; 16+coslso' 2s)) ;(1+cos(120"- 2c:D-lGiII(lb 2ct 78")+ + sin(?s' - 2d + ?s')) = f,. f,"n2" -f,-!*s(eo" + s0" + 2d) -; sin( 2c)- - | cost9o" - 60' - 2ct = l sin 2a - 1sint30' . 2ot r lsin 2c - 1cosr60'- 2at = sin zc + ] cos(so' - (30' + 2a)) j cos(60" - 2o) = = sin2o + ]cos(60' 2o) lcos(60'- 2cr) = sin2cr. 756. I ) r 6. /f, stn zo. stn no. sin ao" = a JI sin zo". I tcos+o. cos 120"r = ,"6flsinr-2o'r - sin60' l, I srnzo' ==aJ3lsin2o""osao. rsi.zo".r.] =, ,, J 2 = n"6l -1"i"20"-1.@.'"r"ro'l aJs. J3 s, 2 2 2 2 ) 4 liliiiiiiif:iil: ATTEEPA Mep3reK A, r. ra iH. AxaAeMi.rH].ri piaeHb tl, 425 " i["."(;..) -(; - "))J ["-[(;. ").[; - "))J = ;*"'* - ;"""; = = !"o"zo - 1. 24 f) Z. |{cosc - cos3a) + cos3d = coso - cos3cr + cos 3cr = cosq; 1l r/., n1 ld fttl tIs 1tt to n,tl sind-2 ,fsinlt;-ul ; rzll'"i.ll , u)*t r' ,r)t)= .tn n I $n a - s,nl 6.] - s,n CI = sln 6 = t .
  • i I j I I ,i't,,J :::::::ii! ::::i::& #fl:ii:::u I I i i r zsz. I.a"i,'91 "inllso.. ol-lao' "ll,"i"lloo' 1l l:o'-llll'- 2 - 2- iL 2r L 2') t' 2t ' 2tt) = z"i,'9("i,'ao" + sin(so'-,r)) = zsin! j + z"n]*"o = ,r 1r r.l I rcr ) a 0 3d 3(r =sin r2 sinl - o srnL rcr l=b'4 sln +sln 2 2t t2 ) t2 )) 2 2 2 z 2nn4nn6nn.ns sin r .os srn + cos 758. l, 7 7 7 7 7 7 , rrr 3n 3nr 5r f 5r) s,nl 7J-sin I "'"l z.l +s'n 7 ,s,nl 7 l+s,nn 2sinI 7 -sin1+sinn 2' 7 sin 10" sin 5' + sin 20" sin 5' + ... + sin 50'sin 5' 2) sin5" cos5" cos15" + cos15" cos25'+... + cos45' cos55" lepeBipKa: f. r=O;.',4*nO d =0-1; 1= -1, piBgicrL rretrpaB!'Irbga. z.r :; n/i-l:-a- -3 li 2-2' BiAno6i0b:3. 3) (J(3r 4x2r sr] r2x- lr : 6x'z- 15x ax 20 4x' 4x t li 2x'-rlx 21 OiD tzt 4-2-t-21)= 121 r168 289i vr'l?: .r. ll-17 7' *"=t' 't' 3. 22 ' 2.2 2 IlepeBip(a: t. , = z; "|s.7 a. J2.7 a =2.7 +li 5.8 = 15; 1b = lb. ^ - , i, ,. ,-- i,r/'i il , r/, l-il-'=,1 ;1,r. BMpa3HeMa,3Micrv. Bidno6idb: 7. ,,Gr:**r*a 5+,r r-4t , =-; vtr r 3 s''; l{'-r^ =r*z; J5 r ,r J5 '.r 'ic+t2=x'+4r+4;a=4. nepeBipra: x q;Jq- 9=Vt.4:2 t 3i3 3. J5+4 Bidnosidb:4. 761, J]iHinEa SyrKrlis 3aAaHa oopMynolo y = k, + b. CKnaAaeMo c[creMy piBEsflr, i3 ABoMa 3MiHnIIMni l-to* + t' = z.J I top+a=-2., I 3b=O;5h=l.h O,2. L5k+6=1r '2 ll0k+2b=2i OyHnrris 3aAaEa OopMynotu y = O,2t. 762. Hyni OyE(rrii sHa.reHH.E sMiEIIoi 1:, npv $]/"llv ssaqelrHs oyHllqii AopiBdlo€ t 2 r -6 .r'-6=0. ll" Jnll",./e t=o-'' - o: '' --0: I 1- '-"- = Jti: ,r^ =-Jti. 3 .r 3x L3jr,0: x'0; 12. fapMoHi,{Hi Kon}rEaHHs 763.1)A=2,6;h=3u 2)'t=+; P=!3 764,1A=O,6t h=2n; 2) A=Ai k = 7. 765.1) A = 2t k= 2' 2) Ssin10'sin50"sin70' = 4 cos 80" cos 40" sin 40' , sin20' 8 cos 80' cos 40' cos 20" sin 20' sin20' 2cos80"sin80" , sin 160" = I1?!l = r_ sin20' sin20" sin20' cosS' cos55" 2sin5"2sin5' sin 25' 2sin5' 2sin5' 2sin n cosf, +2sin tr "o"3n*2",n n "o"Sn-...*2"i' n ."o"r-7-n 75-o. ---- 19 l9 l9 = ' 2sina 19 2n 4n 2^ 6JI 4n 18r l8n sin rsin -sin srn 1... L sln srfl ,-"'re " le -:ls - le ""ls' ""'ls =:::-!-q " le =I7r-i2zsrn zsrn 19 19 760. 1)' - 3 = ,/;=; (r - sl' = (.vG L)' ; f - 6t = s = x - 1; f - 7' + to = 0; Lr,x, = 16t IlepeBipnai 1. x=Etb 3=u[-r; s=s. 2. r=2i 2 3=nli-1 -1= 1, piBEicrb HerpaBrn6Ha,2 He € ]{opeEeM piBnsHEs. BiAnoqiAb:5. 21 ,!t 4x-x =r l: (JI F4,r-"r ) (jr ll':: l-4r .x'z x^ 2r-ri -2t:'z + 6r =q -2r(r 3l=01r=0a6o.n 3=0;.T=3 426 !it: AITEEPA Mep3neK A. r. ra iH. AKaaeMi.rHnr pieeau iiilillii:i:i:* 7e;7. a=J2' 1" Jhi u lsl 2-"i"e"-**"a'l; "o.,p 2; "ine L' lJ5 J5 / '/5 J5 y = 16 sin(S.,' - 9) &yrlttIris rapMogiqrlor t'=J5; h=s. 5xl2jr)5t2768. .1 - Jb - 12 = J16e 13: e I3l r;sin; - i;-";1, "os+ ,"*: sino ii: ,=tr"*(;-*] ibyE(rris rapMoHi.rsoro Ko,'Barr's.,{ = ls; ft=1. i:iialiilililii AnTEEPA Mep3reK A. r. ra iH. AKaaeMienr,li piBelrh i:.:.N 427 2sin25"sin( 30") 2sina 19 766.1)A=3ik=ni 2) A= 1,5; h = 5. 2, A=:; h=7.
  • 769. 1) a = !rE- + 2i D(d =tli +-); E(y) = (2; +-). fIoMiHs€Mo apr.yMeHr r i BnaqeHEs ibynKqii uicqaun: * = i[ L + 2. Brpa3rMo y.rep$ r: l,Ej = n z:y l=(a-z)st!-(r 2)i + 1 trpu r € [2; +-). 2)v=@+3)r 3; D(y) = R; E(v) = R. ' - (y + 3)5 3; (y + 3)5 =, + 3; y + 3 = {,6 + a; c - 1,8 + 3 - S, 3) v={l!. D@)=(--;0)u (0; +-}; r(y)-( -; 1) u (1; +6). t = !!J; xg=y+r;ty-a=l,aG- tt=1: y=-A npr' .r e {-€: 1) u (1i +*). q ! =1,1; 2t ,(y) = t2; +-); E(y) = to; +*). "=1,6 z; v-2='a !=ra +2Dp"€[0; +-). 77o.' ,5-o ' vt--"; * tt .[ br (-r t1): jr 5: Jrs 1 t'z 23x + 121 - x + 5 =O. r'1- 23,. + 126 =Oi D = 2A'- 4'1 126=529-5O4=25i J o = s. r. =4ij =a.,^ =4-1 =s.'2',2 Ilepeaip&a: t.r=ta; ,ft I s- ,6 -1; I l- ,/14 5 2. r=9: J9-5----:- =tr I = L PiBHicrh HetrpaBr"bEa. ../9 - 5 BidnosiAb:14. zl liGTa+s=i{r+3t. saruisa: {.r+3 =t. It -t t t, 4t-5=oi ]:' _' .l r,=-t:r,=i. Itt t'z= -b O6epBeEa BaMilla: 1.9t+3= 1; r+3= 1;r=-4; Z. i,6+r =S; a + B - 125i x = 122. II€peEipna: t. x - t; a.lJt+e,s i[ay.o1 .lr's: t-r. z. x = t22i 4.{t22+3 t s . ",[-tzz"-e .nz, s; zt =zs. BiAnoeiAb: 4i 122, 771. Hexafi Bapricrb roBapy - r rpn. nicn.s ii niABzqeHrs Ea 30 % BoHa craHoBrrb 130 %, a6o 1,3r rpE. Eicnr 3nn*cenHr Baprocri IIa 30 % BoHa craHosarr ?0 %, a6o 0,7 .(1,3r) = 0,91r ryn. Bapricrr, roBapy BMeHlnunacr Ha (r 0,91r) rpa., qo creHoBsrb 0,09 .pH., s6o Ha I %. 95. TPl,lTOHOMETP]|qHt PtBHgHH9 I HEPTBHOCTI 1. PiaHrHHr cosr=b 772. ll cosr l,* t"r""o"l .2Tn,nezi x=!f, r2nn,neZ: 223 EI; """'=#, '=="'**Y -2ftn.nF zi x --2nn.nez. ::i:::AnrEEPA Mep3rrK A. f. ra iH. Ar<aaer.,ri..Hui piaexs i::i:ii:-::i:i:.:itii:ii +2nn,neZl x = tln -:l+2nn, n ez; r = t!! + 2nr, n eZ; .. I 4l cosxa 5: -r, Jsrccos;-+2nn,r? eZ: ct cosr = di - = 1,04: piBHflHHs xopprriB He Ma.i -. n (n -b) cosr=; u <ft r = i arccos : r 2n. n L t. zzs. tl cosx = f ; t = x arccos * + zm, n e Z.; r = ):!.+ 2nn,n e Z; 2) cosr= -|;l', = * ***(-1). znn. n e z; x = t(n - ^,"",.f,) t z^n.,, z; ( ntx=1Ln tJ .21tn,ncZi x -;,2fln,nczl .l; t t; t, *"'=-)Lr'r r=ra."cosl -1?Jt znn.nezt x = -(n - l)_ zn,, n . z, 3rr x=! +zfin.n€zi nt *o'= f [f = t,r' piB's's' ,.ope',iB re Mae; -- 4 a t) cosx = .-i r=tarcaos:-2nn.neZ. 7z4. tt cosr,*= -f,; B" = t ^,..o,(-r) * 2nn,,.zl tr = *(n - """"o" 1) * znn, n e z; sx = x(n - !) + znn, n e z; ax=+T+2nn.nez: ' = x2{ t!,,.2: zl *.*r=*; !' = .t""""o"@ * 2n n, n ez; !x=+I+2nn,nez; n 12an x=x-+-,nezi b5 3) cos 6r = l;6r=2nn,n.2, '=!!,neZ; al co"?=o; U=!tzn,,o.z, " =1*T, n.r, s) cossr = -|; s,=t*"."(-!)*zn,o.z; n, ='(" - *** l) . 2,,.,. z:, = t([ - ! u"*"!) * znn,,. z, iiii::'...x:i:ifi::: ATrEEPA Mep3nrK A. f. ra iH- AraAeMi{Hrf piBeHb::.::::i 2t 42a 429
  • t , ", ,/:r ' Js x "6fil .nsl -- +Z1tn.n -li 3,' 3 3 3 3 3 r=t3arccos@+6nn-neZ. 3 775. 1) cos2x = f,; 2r = t arccos!+ 2nn, n e Z; 2x = !! + 2nn, n e Z; )T_ x=!6+^n'neLi ' -E ' f JA) 2) cos" ,": f =-arccosl '- )t2nn.nczi - ( ,5 1= rfr a'c.o. "j] + znn n -z: i ln i J+znr' n.z: L=xl1+zn,nez; x = +ff +:rlnn, n ez; B) *"?= t; !=n+2nn,nez, '=!*!,".2. 776. rl cosn-t) t, ' ';-.,*-"* 2rn.n. zi ,-I==I ^.,.,. ,=ti [+2""."e2; zr "osln rl -J3, "o"1, n' 6, *- n ==u.".o"6 2nn,nczi A I 2 4) 2 4 2 ' - 1=.1 '2nn,n-zi' ' )-!-znn-n-z,4664 3f *"[;-rJ =-r x 2 n 2nn.ncz: t=n z 2nn.ncz: x 6,1+12-12nn,n-7, ar zcosl n rxl+r=o: zcoslar "l -', -"1a" "l I'----8 ) 8' 2 n lr - s' n :l^-".""""f] ,z^n.n.tiJn--=larccosl 2)-21n.n.zt a 2) ,,-l='[^ I) ,,^.,-,, *-l=.? 2nn.n.z: 2an2nfiz^n ,r -j - 8-zfin.ncz: t -g,2q+ S.n-L. zzz.u.""([ *) =', *"[*-3) =L; 4x !=2nn,nez; qx !,2nn,ncz;,=!-,"!,^ - t;9362 . 1(t Jz) z lz*"li-sj= r: cosl; ,J =-r :a. " ,, " ,=..*""", '') 'r*^.^,t, l"=-ln u,""o"fi1-::tznn,n-z; 2 2) 2 2l | *3h -t-2nn.n.zi t +3^ o-4nn,ncz. 43o iti: AITEEPA Mep3nsKA. r. ra iH. AKaaeMi.{Hrr piaer" :lilliilllii:l:liii 77a.rt cos( x-nl=1, r n + arccost ,znn.n.z' t 6,i 2 6 2 n'un ox. ',' I, *^=!-!=^.366362 [D'r,r =-t ,. -n n zn I3n., =I-I-n=-I-366"362 ,t Ha/oubruun Br{ cMHr.rx KoprHb - 6 . t; I 1; 779. cosl f; 1=rar.cosl -1! *2nn,n.t; 4 2 4 2) {=.1 n-u.""o"V2 I znn,n-z:' .-3J! 'znn.n-zi x--:,ntBnn.n-1. 4 2) 4 4 fipr n = O rt= -31ta 12- 3n. BiAno'iAb: 3n- ' = x! +[+ 2"", " ez. t; 1; 7ao. eos3,r Y, ar . -"--"Y -2nn, n. /t22 n zftn + .n./ 18 3 Ioru =o x. = -4, r =4,la ' ra 2 ,:,b ,n2nllnn2nlsr.DDX n l.r I - -: Ja^ = +'r8318'r8318 4a'oMr rpoMi'$Ay Hane*ar6 '.opeEi piBEEriH" -+' #,*'#. BiAno6iAb: .{orrptr. 781. "."1*+rl =-!, ,- " . -..""."l. t) 2o,.,-2, 12l 2 12 2) l n2nr. '_=- ,( - arccos - t a znn. n lt xt ! 2nn.nc7: 12 2) t2 3 2n n 2nn + he/ 3123 2nngn2nfr7nllDr n = ll i 3 12 t2' '"' 3 12 t2 2n n 15n 5JI 2n ft 31tr ltnu r I I -trr=-- t2n 312 124'3t2 t2 2n n 39,r 13r 2n n 55n LIoJ1n:2 x t4fi -t x-=_- -4n312 124',312 t2 n7nn5nn3larl3tr_-?4n: --<. <4'I: - _ _4n: <4'I. 6126461264 ab cLb al iilriiitlii::ji A'TEEPA Mep3neK A. r. ra iH. AKaAeMi.rnr4i piaexu il.l,| a3r ^n2nn;tx=1: + .ne/,- 63 I il I I
  • r"..t, {1lo'..... ^.3', r:x+2=o;D=24 4.3.z=rt JD=1; ,,=fi=r, l3r'-5x+2>oi 3) sin 5r = 1;5r=!+2nn,neZ; "=L+2-!!,r.7, +y "t"1 a'y=f,, sinsr=-J; r"=r tr"**r( ?),n,,.2; {-11'1 2 ir -arcstn o L 7r[r'cz. ,"r. r, "rn"* = S, 2.r ( 1," arcsin !, nn. n, z. 2x = t-tti ft nn.n c z. , = r-.' x' "1' , .2, 2t sin{=01 nn,ntz: x Tnn.nczi s) "t-?=,+j ? = c'r"-*'[-.4) + nn. n ez) ?! = glyu L a no,,1az; x=(,11*14a!!!,n.y. tae. ri "t"(,-fi) =!, . [= ctr ^,csin@ +nn,n ez; t = (-11" ! a! 1 ,n, n.7t 2r sinll-xl' 6, .i.l ,-nl Ja L8 r 2'---!'' 8/ 2' 1=1-1fi!1!1no.o67.. 38 s) "i'(;+r= 1, i*t= -X*znn,,ez; != -!-1a2nn,,.t, ',= -! a+en ,,ez; .- , ",(#-,, =#, ",(*-#) = -9, a*-lr, = r """'".1"(-.f) , n.nczi sx=(-1"^f,- lr, r,.^cz: x=t. tf 'a*-I +ftn . n =7,.12363 zos. ry "i"[s'- ') =t; ex-{;=-!a2n ,o.z; s'=-!*#+21tn,n€z; 8x= -9! +znn, n ez; ,= i"ni,".z: ,r "'(; -.) = -1, f -+ = crr. **i,(- !) * *,,,. z; t - n - ctr" i * "", ". z; ! = t-tt,,' f, * a, + nn, n e zi r = (-r"'t ! + 20 + lnn, n e z. :!lt!tjittt;i1: AITEEPA MepsreK A. r. ra iH, AKaaeMieHnt piBeHb :-t{ 43g r^=9--L=lt &r t)l r-:l>0.' 2.3 3 3/ Po3B'sryFMo sepiBEicrE veroaoM iErepBa"riB: Tr Bianosidb: D(y) =lu i lu (tr + -t. L n) 2t 1" ^ "'13-xl(3 | xl>oixz-21 [-r+2+0; (3 - r)(3 + r) = 0; ,1 = 3; t, = -3. BiAnoeiAb: D(s) = | 3; 2) u (2i 31. lr'z+5:-1+>0. 3 I -rz+5x- 14=0: lx' 64 * o: lx, x,= 14: ----T /z:/.-=--l<:<RK4 03 l' 2 (x+7{, 2>Oik- 8)(af 8)*0; t+8tt+ 8- BiAnosiAb: D(y, = (--; -8) u ( 8; 7l !, [2; 8) !.](8; +-). n, {a -2f," o' zJi < r; 4.r< l6i x<4i } > o. L-r > o: BiAnosiqb: D(gt = loi 41. 2. P|BHTHHq sinx- b 784. 1) sinr ft; "=t-ll'a,csin fi tnn.n.z, x 't-r't^f,'nn.ncz: 2) sin.r=-+: ' (-rr"*"h[ J;).^,.,.r, t. t.|'][-nn,nez: sr "in* - l, r =(-1t'arcsinl +nn, n eZ; 4t sinr = J2 {Jz - t.n:r.n ' rlr piBE'EEr Kopegis I'e Ma€. zas. r) sinr=|; r=( 1)"arcsin|+nn,nez; t=(-t"1+nn,nez; E(t-.r zr "in*=-121, .=r rr,*"r'l-f.J 'rn,ncz: x=( lt^")-nn.nezt sl si",=f ; x=( rY ansir !! + rv.,nez; 4) sin r = 1,5; piBEaIIIIs riopeHiB Ee Ma€. z8o. r) snf = ]' f =co"**t( L)*nn.o.z' l= t-r"'l+,o, n.z; r. = (-16n + 6nn, n.Z; ,) "in 4J f: 4rr = ,-u' "'"",' Jt +nn.nezt a{ -etri*n^.,,2t '=61y!+4!,,e2; 432 t :::An|EEPA Mep3reKa. r. ra iH. AKaaeMiqgr4fi piaegb iti:jtlttlit::iii n I -Al-r-t={-1rarcsinl - )+ fin. n ezi
  • '/ J:)7e0. sin{r+ll "i, '.i=,-rf arcsin( ::J ,nn.nc?: t = 1 ty" ! -! ', nn, n.7. rp n=o jr=( ,,: x=-:-x=-3, npr n= r -!=(-1)!1 it"= #r"=# p16,oui6o. !!!. 12 rn'. "''("-,!) = ,, * ir=-X.r",.^.2, z,=-I- ls*z^^.,<2, *=_4!+znn,nez,, " = _ff *2{, n.z, ttDnr=o.r -13n, rro,,=t '=.13n,2" lll '9090390 3i6noui6o -1J1. 90 -lrzsz. rt Ja.in'*"o"' z1,z: Jr!.",n'* r -"' 1, ",nr'.o"I rcos' s'n1=t: "t"lr, "l ,, x.!=.nn.ncz:6 6 ' 6' 6 2 x =I f,+nn, nez: x =! + nn,n ez: z) .Esinr .Ecos.,c=11:2; ' , * *", *=;t "i,,,"."1 *","r"1=i' "',(., I)=i,,-i=,1).arcsin!+nn,nez; x = ClY ! +! + nn, n <Zi '.' rtrvE3) ssin'-+ J3cos; 3i:2J3: 'r"-stn, r icos, .i; n x n Je ,, ^, .Itsrn2cos6 rcosrs'nd=; I srn|2,6J= -2 I ./r ' - '; Fi ,rcs1n re .' n,?. 2 6 2, i= r t [- i- "^. ^ ,2, x = (-1'2J! ,! + 2nn, n eZ. ze3. r) sinr-16cos"-r ,r, j"r,-f *",=|, "i^,*"1--","*3 =;, "'nf" ;l l, , i=r-r, "-"r"] nn.atzi x=t-tt'n,lrnn.ncz. 2) sin-y+cosr ='El,'Et | "i", -L"o"r I: sj n r cos I , cos x sn lr l,' Jz- J:---- ' -' "---4 ""-" 4 Jt' 434 ii:: AIfEEPA Mep3Iex A. f. ra iH. AKaaeMiqH]an piBeHb :::::::;i::::::::ii::i:: "*[,. ;.) = *,," i = c,r.***f +,h. n ezi '- ( D" X -X* "", ". z. ^o. "'"['-;) =], ,-I=( u.a,."ini+nn.,ez; npsn=ox=1+I=1. 6 3 2' ,+f,=t tt,*tn, nez: t=gty!+!+nn,nez; nplr n = Lr.{ t} I r:. r='ll; npr n = 2 r= r-lt'?I+1*Zr= I-,6 3,_,._2 _ Hp BxoAurb y npoMirnoki npun -t ! =r-rr | -". lr= tu "p,n= 2: "=(-r).;-; ,"=_+ _ ,,e BxoaHrL y npoMr*ox. -^ 5 ft 7^ 626 7es. sin3x =f , ", , rf u.."in:2 , tin,n-zi ax= t-tf ,nn.nez: ,=1ry$*!!,".2; nprr=0.r={ 1f 1=a, 12 12 npun t.r I rr'. 'I.+t=31 =n.12 3 t2 4' np n=-l;=1-11 "1-4= -8.' 12 ?i 12- .pvn= 2 r r-1r..!-':=-!1,,=-3,x, { l)J " -,,-l!1,t2 3 t2 - t2 ' 12, n=- 4.x=t tl' n -1n-- I5T. t2 3 t2' ,n 2n gn ti_.t = tZ He BxonHrr, y npoMi)KoH. Biano6i0b: rtich. zgo. rr 9=@=2.,E. J33 zr rq_ 15.V5 _15if _.,r.' v2b y'5" i6 5 -'v" .. Bo ao Jo goV6 -.-"' m-F G= i =ovor ot -- 12- l2('4? J5) Lz(Jrz - v;) r, Jti ,5 ("rrz r"6lt,rz-us) - rz-s =vi/-v5: ri:ri::::iiii::i: A,lfE6pA Mep3nrx A. f. ra iH. AKaAeMieHri piBexb ;i::: I 435
  • r -. 16 16((f)' {?.r) '' itt - = (vz,.J@f Vr;il = = zltg zlF zj ", 2t zr (.,,6 * 'E)-' {/r5 - Vio - {a - (Vs, -,6 .8 , r/2,)(Vr , Vz) a2 I ro(Vns -,F * 1) - ro(Jas - {,4 * 1) (J7)' * r' 8 - u({:r*u{t) = "a1 u n r;,12. lx.gxmors0.'197- lt u=l" [4x x', *rqo r > 0. y = t, rpaoi& rp€Ma, sria trpoxoarIrb qepe3 roqrcn (0; 0); ( 2j 2); y = -tu + 4r, ryaoil( trapa6ona s BepmrEom ,,",,, -=_L. ^=___L=2,' 2a 2(1) n--22+4.2=4;(2,4r. To.rlir r€pertrEy s Biccro Ot: -t2 + 4z - ot -r(x - 4) = oi tt = oi t, = 4. Toqrcl,l repertrEy - (0; 0); (4; 0). Ia| ,axutox<-2, t.r2) y=l ir,rlcqo-2s-rs0. lV.x.sxnox'0. 1. IIprt< 2 y=-4, rpa6ix - rinepoo.na. 2. llpt -2 3 z 3 O y = -t, rpa(bilr - rpdMa,' afta poxoarrrb qepe3 ro.rKr (-2; 2); (0; 0). 3. flp{ r > 0 y = {,6, rpa4irc uo6y,cyeMo Ba aotroMororo ra6nn4i. 3. PiBHTHHq tgx= b i clgx= b 798. 1) tg.r =."6; r=arctg^'E+nn,neZ; 26=!+rn,nez; zr te' vj, ' -*cl.-vJ]--, ncZ: x=-!+nn.n=Z; 4) tex = 5; t=aJ€tg'+Tn,nezl E r1 "tgr- vJ, tg=v6; r=*"tg1,6-nn.neZ: x-l .nn,nez, 6) ctgr = -1; lg r = -li n = srclg( l) + nn, n e Zt " = -! + n", " e Z: h t J:) - rzt ctg.r=-u6: U*=-f, *=arcwl i, I nn,nFzi r - -'d-",,,.2, 436 ltl AIrEEPA Mep3reKA. r. ra iH. AxaseMiqrrlrfi piaert l{;{ilii::ritltl q c4x =."F; t",=*, ,=**"*+nn,nez, 9) ctg:c = 0; t=!+nn,neZ. 799, 1) tgr=1; x=arctg]'+nn,neZ: ,=!+nn,neZl zt rc, =f: *=-"te@*n,,,. z: x=n t nn,ncZ: s) ter--a6; t = "utg( h+"","e2; t=-!+nn,neZ; 4 tgx-2:. x=aralg2 ^n,nczi 5) ctgr=u[; tg Jj-, "=***f -ftn.nezi ,=[*^^,n.2, u, **r= f, Wr= nE; " = u."te (-nE) + n,,, o ez; r=-L+nn,nez; 7, tex = O; x=nn,nEZ. 8OO. l) tg2r= l: 2I=arcrgl-nn.n eZ: 2x -nn.neZ; ,neZ; ') te; =;; !=*.tet,rn,n.z; x =sarcts*+vnn,nez: 3) t"[ a4)='6, t"f=-"E, !=a,.tg(-Ji)+nn,,ez; 7x tt - 41 4fin -:=- - tTn,ncL: ,.. :_= ,nez;43277 4l cLg-=Oi 2 2-nn.ncZi x=fi-2ftn.neZl 16nnx = - arcig +;-,neZi. I;B 6) c!s(-gr) = uj, "tss"=-uj, tgsx=-/3; Sx=a."ug(-Jr) | nn. n czi sr = -! + nn, n ez;, = -ff *!,,.2. 8O1,11 tg9a = 6; ?r=nn,neZ; r=4!.neZ; t; .- I t;, 2t cLs' '6: tgl=-w. ;=*",c[-v3{] .-. ne z: }=-!+nn,na7, x=-L+2nn,neZ; B) ctc;r=b; tu|, =It X'=*"el+nn,nez; '-|u"tsL*,n,o.7. - G .Js n n802. 1) rcf3.r-;;J f,*-i! arctsrs+nn,rez: ax=')t',. -nn.ncz: ^ 11 _ llltn|Jx= 4-nn.neZ: x= t2' Br.nczi i:i:lifjii:illit: AITE6PA Mep3rrKA. r. ra iH. Axa,qeMi.rHri piBeHb :.{i 437 8 -4 v 0,5 1 2 1 16 u 1
  • / tr 8o3. 1' telr+iJ ti ! + ;- arctsl + nn' n ' zi -7t2x = - 6 t nn, n - Li t = -- + :2. n. 7i npu n=o x=-12i -fin7fi '12212 "p",.-2,=--o.-^ 1:: Fe Bxoa,{rb y trpoM,){oKi'12 12 ,rrJI5JInDlIr=l r= +-=-.'12212 npun 2x. .'^'n=9 - He Bxoa'rr6 y rpoMixoK;'12 12 12r2)12t24 Bidnosidb: n . 4 Bo7. E ! = Ji; | = a,.ts.ls + nn, n e z: ! = I + nn, n e z: x = 2! + znn, n e z: 2n npnr, 0I a: 2n 4fi npl...n=-t x 3 z 3: 2T lotr np, n=-2 x- 3 4tr 3 - HF sxoAxrby npoMirltor: ,'o"n=1,=?!*2n=9!, - 2n 14fi npqn=Z x=-+4n- .r He Bxorurr, y npoMilxok: 2n ( 4n aft 6ft + l+ = =2n.3 ! 3/ 3 3 BiAnoeiAb: 2it. 8o8. {x + d)(Lg.r - J3) or r o . 0: .r = -a a6o ugr J: or ,r arcte.,6-nn.n cz. x ntnn,nel. -3 PiBHsHHs ig-r J: 0 "" npori*,"r /- n [u: ] Ma€ oal'n xoprnb - -. Ulo6 aa"e piennnsa Ma,1o onrH xopiHb. norpi6eo. ilroO -a=Ir a I Bidnolidb: Eopt o=-n,o. ft o'g. 809. (r a)(te r + 1) = 0; r o=0:r=aa6otgx'l O; 1g.r '1; t=-!-nn.n.2. PiBET,,E' ts ' + 1 = o "" "n"*,**" [- ], o) piBH.EEHs Mano oAr-rE nopilr6, trorpi6Ho, qo6 Bionoliab: rrp*t "= !;"< !;">0. 2) te(3 - 2' = 2i tg(zt 3=-2r2x 3 = srcLe e2 + nn' n e z: 2r = arctg (-2) + 3 + nn, .Z; : = I arcte(-2) + 1, 5 + !,,. z; * = - f;^r"tc 2 + !'5 + T, n e z. i) Jscre(s,-{J re -o: nels,'iJ Jr: uslrx'li= f' *. 3 = *""(-f) - n,,, e z; rx = -f,-i + nn' n e z; 5x = -L + nn, n e z; +-.naL.. 10 5 , "'-[: -;) = +, *(; :) = -,6, !-i= **s(-15 *,,.,.2; L--!*X*nn,n.z; ,=-n+!*znn,oez; r= f,+ snn, n ez. fir! x= --+n,nELa 2) ctea-3x=2; is(4-3r)=;; E@' .4:) = -;t sx-a= arctg!+nn,ne s, = - a,.teI+ E+ nn, ".2. ' = -+*&e;*tt!, ".2, 3) 3te(3' + 1) -.,6 = o; tg(arc+r1=f; 3"+t=atc4:$+nn,nez; Bx - ! - t + nn, n ez.' = ft- !.!, ". z. 804. te 4.,. = li 4, = arctg 1 + nn, n e Z, ."rr=O r=3,' 16 nnEtf,nu n=l x= +-= i '16416 nnvn=2 r=-+ = : '1621ti 'I 3,r 13n nnrn=:J x= + =-_' 16 4 t6 +-,neLi16 4 n l7n np{n 4x--: '^ ;;t - He Bxor!,rb y opovi)xoH. Bidro6idb. .rorxpx HopeHi. .i; aos. ctsf= uJ, ,*; --Jt, i--."*( Jr)--., ELi t= n'ynn-n-Li npvn=0r fi- He BxoA rb y npoMi)*ox: npttn=1t= n+3n=2fi: Rpvn-2x= tr I6'I=5,I He BxoA[rB y EpoMi]HoR. BiAnosiAb: 0qrd]l. 806. crg2:r=-./!; tsz'=-f ; ,"=^,.@( @)*no,n.z, 'lt ^4t=-+nn-neLi '4 Ma€ oar-{E Rop1ts6 --. t[ob,4axe 4 n 4 438 i::J AIIEEPA MepsnqK A. r. ra iH. AKaaeMiq{lir piBeHb i:i:::r:li:it{lillj ATTEEPA Mep3rrK a. r. ra iH. AKaaeMi.{HrF piBeHh t:i:l 439
  • 'l A1O. trIo6 rpaoi& OyHriaii 6l'8 ctrMerpr.rqElri siaHocEo oci &oopaltlrar' OvlrHqin no BI{HIIA 6YTII trAPHOIO. q-x' " 4-l x)' 4-x' I I /(r) cost: rl ir' = cos(2 ( .rJJ cos2.r' OyE&qis trapsa, ryaabirc cr.IMerplrqHri BiAHocBo oci Oy. sin r sin(-.r) sin.t 2J l{})-, i ll-x)=:=' l-cos.r I lcG(-.r) l-cos.r <DyrIKrIrs Eeraptra, ryaoirc Ee cvMerpn'rE ii Bianocso oci Oy. st t@) = dr- + d2 + t; tt-'> = E-t-"l + lz + t i = Ei + tE - ".(DyHFirIis rapEa, rpaoiK caMerplrqHr'ri BiAEocEo oci Oy. 4) f(x) = x' E x' f( x) = (-t)' ts(-x = -x' te r. (Dys&qis EenapEa, rpaoil{ He csMerpt{qHsfi BiAHocEo oqi Oy. 811.1f(t)=f + 3i t e IOt +4i t = g' + 4; a" = * 4' u=$ a trprre [4; +-); 2flxl- 'z-1;t€(-;Olit=A' 1;U'=x+1t A= Jx+1, t€[ 1;+-); s f(r')={V; re( -;ol; a="Ft u= vF, re l0; +-). 4. Oyxxr{ii y = arccos x; y= arcsin x' y = arctg x; y = arcctg x -, . (n ^ trl 3r nt " Ji/l srllt -+2, -sm_=sintn_ -cih_=- 4 4) 4 4/ 4 2 81s. 1) tg 0 = 0; 2r "i.1=@,32 / _ 3r cosl 2.1 l= .".1 = o, I 4,] 2 ar "tn[z t'l = cts4 = o: - 4,r -2 5) ts(2'i) = b; 6r cosl n-11+lll="".r= r, 3 3,/ 812. 1) Hi; 4) rarc; ?) si; lO) 9a+1=r. rar: 44 13) arcts(-1) = -:, si; 813. 1) I{e icEye, si; 4) raK; 7) arccosO = I. si: 2 10) ralc; 13) ri; tr !!."-! ="!L . "i t2l 43 2 14) rax; 2, Iz$i 5) ran; 8) arccos 1 = 0' Hii 11) raIi; 1t n 5r, ra);+6=-.ra1c; 3) raK; "/nti) - l -- l= --. Ilr:'33,r I 9) ra&; arccts0=I.si:'2 r .3r _.13n -r 3 4 t2'"" 3) ra(; 6) ran; 9) se icEye, si; 12) arctg Q = 0, IIi; 15) rax. 2 ait 5) Ei; 8) raft; rr+-+ fi- | 3 t 6) 4 3) 3 4' n -+2 n 4. 15) 663 6n+3n-3fi+ 4n-r 14n 7n 12 12A 814. 1) cic; = L ,) -"[,;J =ot " *"(;9=+' 619. 11 -I..s14-,1=I'6 46 4 zt zln-!1. s.1*n.l-I)=2.sft sft 4 10,I-lon-l2n -'-1" 6J -3'.2t-'e e-T= a-=-2" A2O. l I < t - 2 < 1; 1 < r < 3; D(y) = [1i 3l; 2t -1<,'- 10<1; 9<',<11; B<:l<."{J; lfvl = l-Jii; - s] u [s; "/i1]; rr t'f sr, -2s1<2t r< -j'u.'= |,og1=y*r-Lp1f,, a, 4 -1< Ji <t; 0 < r < 1; ,(y) = [0; 1]; 5t D(y) = Ri 6) x / 5: D(y) = (--: -5) u ( 5i -)i 7lx 2>0ix>-2:D(gl L2t *)l [-'' .1.,S) I--x-" ir> l;D(?)=[1; +-). lr-1>o; A21, Ir -1 < x + 2 < lj -g < r < -1; D(y) = t 3; -11; z) rs:<L -:= 1. :, Dtvt=(-,-:),'l:.'-J,3x2x2r 3) -1s J.! < 1; 0 <, < 1; D(y) = t0; 1l; 4, x 3>0; t>3: D(y) = [3; +-); ::i*iir::itttil: A'TEEPA Mep3ncKA. r. ra ifl. AKaAeMiqHr,rfi piBeHb li.l 44.1 a) cre(2 (n-a"ccteJtf)="*lt ("-f lJ ="1"101 =".,un ""[r^ ])= .11 Jt= _ crge = _;: rr "i.ls.I-1ll = "r"r nr=-r,' | 3/./ I / nl n) I r' !56) telz L--l I 6.J - tcl-6I - t: 440 l$: AITEEPA Mep3nrKa. r. ra iE. AKaaeMi'{Hr'rr pieens llillilif.il{!:l zr "o"lr.n,l" ".""."111 -"o"1,,,, n' I 7t 'r I r 2,) , r-51=coslz'I s.] =*"5=z' eto. rl "o"],u.""o" 1l. lr 2ta: 3t tr: 4t I 3,/ 3 4 2 817. 1) 818. 1) zr!2 4* 4:: 4) n. 3n+6rt+2rt+6fi-n 16?! 8'r
  • fl D(v = R; x+7+O;t+ 7;D(V)=(-; -7)u( 7i +-)i I' x-1-r. lo-1=r.,,r, to,,r. lx>0i l.r>o: ezz. r) -]<u."si,'' <!; o < ",.'i"t +! <'I; v.,^ = 0; v^,., = 7.; 2) 0. arccosr. n:2sarccos.r+ 2<n t 2iy... 2i 9,,," fi- 2i g) -1<u.""i,'r<;; n<2 arcsinrsn; "-I<z**r' 3=n-3t 4nn2fi4n2n --i.zu'."int t's,s", -T: ,"^ = a, 1114t 0 arccos x'n, ur."o"r t n, Y- = n. 823. 1)0sarccosJ.<rx; n < erccos r. + t! < 2n; g, ',= n; y,,^,= 2n; z -! < u'""in'<X; -L z < u'csin" <! z; s-,, = |-zt o-,"=X, ", 3) 0 < arccos, < 7t; 0 < 3 arccos ,. < 3fi; rr fi 19r ; : 3 arccos ,r r 6 i 3 'r 6i 9"." 6. C",. 6 a24.1) J;>o; o<arccos,4<|; z<arccosG+z<]+ 2; v,",= 2: - .E; ,E; zt ')',*'t,*: ir 0t Jarcsirx:ll' : u.,, =0i v,' ="r" 82s. 1) t>0; o<u.""i,''4<l; 4 < a.csin G + 4 < j + 4; v",'= 4: 21 0 - arccos,r ' o, O sl6.cco"r: Jn. sr6. r) *"[***;)= pe. 1% E'' 1J15zr tel**nJ) = ",,. ', "*(***]) = F;G;r = lIH( t22) cts arccos- ="t t3) A2a. 1) 16 3r3 - 10 = 0. SaMiHa: ts = t. t2 - 3t 20 = 0; t1= 5i t,= 2- O6eptr€lra 3aMiga: f =5a6ox3= 2; x,=lli; ,"=<l Z=-:12' Bdno1idh: !2i 6. 442 i::l: AITEEPA Mep3neK A. r- ra iH. AxaaeMi'{Hhr pieenr lil:iiii::iili:iiii 5) 6) 7' 2t l:lxttl -3V,rr4 =28. Sar,aiHa: (G+a t.t?tBt .28 Ot!t=.7.t2.4. O6epEeHa saMiEa: {rtS=-l - &opeIIiB HeMae; li+4=4; x+ 4=286t r = 252. BiAno6iAb:252. T 4'r .4. L=5. 3r,i,u. ?I I ,_ x 2x+7 [r' -si ++=0, ]l = r, r, =a. lr+0, lt*0. o6ep'e'a seMiHa: 4j] =t; z'+1=rr"= yt2"'1 =4,tx 2x + 1= 4xt 2t= 1;x=O,5. Bidno6idb: It O,5. 4) r'+x-2 {x' t-2=8 z. gr-1"", G' *-z = t. t, - t - 6 = o: t1 = -2; t, = z- O6epEeEe 3aMina: r[S *t-Z=-Z; ftopeuiB HeMa€; .,8 *t-Z=Z; x2+r-Z=g; ,,+ ,-11=o;D=1 4.(-1.1r=45: Jo =a,,E: ,,= t-:n, ""= tr:.lt - 1-3.6 t+3.6 22 829. /(-5)=( 5,16 0:g(21=2" Oigtl)=l:g( t) 1. Bidno6idb: et I ): E{l ti /(2)r /{ 5,, 830. CrnaB Macob 36 rr uicrrrr 45 % Miai, rqo craHoB'rb 36 . 0,45 = 16,2 Kr. flIc4o Ao Irboro crnaBy AoAars r Kr MiAi, ro iroro Maca cranoBmb (36 + r) !tr, a MiAi B nr,o, My 60 %, qo craRoBnrb 0,6(36 + ,) Ir.. CKna{a€Mo piBHnEEs: 0,6(36 + r:l=16,2+ t;21,6 +0,6t=16,2+ tcr 0,6 t - r=16,2 21,6i -0,4x = 5,4: r = 13,5. Btdtlo6,ab: 13,5 llr MiAi. 5. TplroHoMerplr.+ri piexiurr, r<i aaoAirbcr Ao anre6pai'qHl4x 831. 1) SaMiHa: sin r = t, ztz + t - I = Oi D = 1 - 4. 2 ( l = 9: JD s; r,=-l-q r, r"= 13 | 2.2 2.2 2' O6epHeHa 3aMiEa: siri r = -1; n1 x,-'t t2nk-htz:: "i"' j, "=r-rr,X ", ,"t. BiAnoliAb: C1)'! + nn, n eZ; -! + 2nh, k eZ. 2) SaMiHa: cos a = t. 2t, - 5t 3 = O; D 25-4.2.( 3t 25 F 24=49: JD t, t,=5rtl a, r,=!r.l ) O6€pIIeIIa saMiEa: cos a = 3, (opeHiB EeMa€; "o""=-.1, r -fr r,..." t.l ., 2nn.n-zt x. !2n t2nn.n 7.. 2 2) 3 Bidnoaidt: 14 +2nn. n eZ. 3 3) SaNriEai sin , = t. t, + 2t 3 = O: tt= 3; t,= L O6epHeHa 3aMina: sin 3r = 3, KopeHiB H€Ma€j sin 3, = 1: iiiiii{lilllii: UresPA Mep3rrx A. r. ra iH. AKaaeMi.rnri piBeHb ,:t 44s ,*1-s=0, {j*=0, ,, =+2. ,, =L+4.
  • fi zftn 3x=:+zfin,n(Zi x= 6. 3:,ncZ. Bi.lnoaial6: :+-.nez. 4) SaMiHaftgr=r. t' - 2t - 3 = 0', t1= 3i t2= -1. O6epneEa saMiHai tg r = 3; t = arctg 3 + fln, n e Z; tg x = 1; r = arctg (-1) + 'rt, he Zi t=-I+nk,heZ. Bi()nosidb: arct! 3 + fini fr + flh, n, h'2.-4 5) 3a{ina: ctg 2t= r. 3t' + t - 4 = Oi D = t - 4.3. (-4): 4e; uO =tt t,=-j| = -!t O6epEeHa 3aMiBa: 433- cte2x = -;i tgzx=-=i 2x = - arcLg i t nn, n c Zi cLg 2x = li lg 2x = li 2t = arctg 1 + |th, h e Zl 7fi,th fi nh -x= +-,h€L, a= a+r,REa. l3rrztrft[ Bidnosidb: - ;arcLc;+ ;t ;- :-; , n, h e z- 6) SaMiEa: cos I = l. }t'z + 5t - 2 = Oi 4 D =2i - 4.s.{-i)=4s: 1o =t, t,=fi . -z; O6eDAeHa 3aMilta: cosl = _ 2, xopesie uemae; '4 -"f=|, i = t**osl+znn, nez; r = +4zrctoe!+ am, n ez. Bianoaiaa: !4 arccoaf, + 8nn, n ez. 832. r) 2 sin't - 3 sin t + 1= 0.3aMiEa: sin, = t.2t'z'3t + 1=Oi D = s - 4. 2. t = 1; ln =1; r, =f;j =t r,=T: =i o6ep*esa 3aMiaa: sint=l; x=!+2nn,n.rt "tr t =f,, Biatuolilb ;+ 2nni F1)' [ + nk, n, k e z. 2) BardiBa: cos 2.x = t. 2t''t | =O; D-1 4 2 (-t)=9: JD=3; 1,=L1!=1; ,,=;;= ; O6epEesA 3aMiEa: cos 21 = lt 2t = zfin, n e Zi x = fin, n e Zi """2' = -tt 2r=rarccos( 1)-z*.*.2, 2x=x?+znk,nez; r = tL + nh. heZ. 3 Bianosilb: nn !;+ ftk, n, h eZ. 444 l:::l MTEEPA Mep3rr|( A. r. ra iH. AKaAeMi,{H'i piBeHb ii:i!#idlllii 3) SaMiHa: tg r = r. 4t, - t - g = O, D=1-4.4-(-r)=as; JE =7; O6epEer€ rar.iEa: tg r = 1i 1-7 3 = tt = -i' z=!+nn,neZ; tgr = -9; r = -arct "l* nu, u r t. Bidnolnb: X+ nn; -*cttl+ ah, n, k ez. 4) Sauina: ctg{=1. Bt, - t - 2 = Ot D = 1 - 4 . A . (-2, = Zb; JD=s; t,. l-l!=1. ,, =r-5 , ? ' 2.3 ' 2.3 3. O6epEena saMiria: ctEl = t, 1=O*nn,neZ; r=4+Bnn,neZ; "*i = -?' ts; = -;; ; = -*"t sf, + n*. * e z: r = -t *cLcf,+ ''-h. k e z. Bi}noarlo: 4 + Snni -Barctg! + Bnh, n, h eZ. 833. Aerlri rrir piBBrsE - oAEopiABi. glclqo IlptrIryc"rrr, qo cos , = O, ro sin , = O, oAFoqacEo rli ABi piBHocTi se Morri]"r,r, BrrxoEyBarrrcs, ocrcirbrin cog2 , + sins , = I,ToMy cos .r * 0. 834. 1)sior- cosr=0l: cos r; tg.r 1=O;tgr=l; r=!+nn,neZ; 2) Jfein++cos.r=ol:cos:; Jttg"r+r=0, tc"=-;br x = _!+nn,nez; 3) 3 sin r= 2cos.rl: coatiatgt=2; tet=!; t=*.tef,+xn,nez; 4) Acos2x-sin2r= 0i:cos2.t; 4 tg2x=OrtE2r=4: 2.=a:(jts4+ftn,nez; l.= I*ctea+T, n ez; 5) sin;+5cos;=01:cosf; tef +r=o; tei= ^s; i=-*"teb+nn,nez;t=-3arclg5+1i.n,neZ; 6) sin'?.r - 5sin.t cos r + 4cos? r = 0 | : cos2.ri tg2 r - 5tg, + 4 = O. SaMisa: tg.r t.t,-it t 4=Oi fr , l:r,=4. - O6epEeEa BaMiEa: tg r = li r = srctg I + nn, n e Z: t = I+ nn, n eZ; tg z = 4; x = arclg 4 + ith, k e Z. Bilnoaidt !nn: arctg 4 + Itk, n, h e Z, ?) sin, ; - ssin;cos ! * z*." i = o;l** i, E ; _ s E ; + 2 = o. Saruira: tgf, = r. *-Bt+2=Oit1=2it,=t. O6epEeHa BaMiEa: Le i = tt i = ^r.tc t t nn, n e Z; | = ! + n71, n e Z; x = ! + 2nn, n e z; j:i:lttilJii::ti: ATTEEPA MepsrrKA. r. ra iH. AKaAe&ti.{Hri piBerb rt:j 445 -l +7 lsfln ^.cts-+-.neLi2 -4 2 -5+7 1 1+7 2.4 -'
  • E;=2t t= arcrez+ nk, k ezi t = zarctg 2 + 2nh' k e z' Bi(Jnosdb: ;+2nt 2arcts 2 | 2flk' n' h - z' 8) 3 sin'.2 216 sin r cos, + cos2 ' = 0 : cos" x; te' x - z^13 Lg t + 1 = O' BaNriHai ts,=t. 3f zJat+1'=oi o=( zJa)" -t a-t=o; ts'=f; r=*""tsf +nn' nez, x =I+ nn,n ez 834. 1) sin, + cos.I = 0 : cos r; tg, + 1 = 0; tg' = -1; t ='! + nn' n eZ; 2) sinr.- J3 cos"r 0:cosx: ter-J3 '0: tsx J3: ' i' "^''-z' 3) 2 sin ir + cos, = 0l: cos t;2tg Jr + 1= 0; r1 lgx=-.i x= arctg +nn,neLi 4) cos 4jr 3sin 4' = 0 | : cos 4r; 1 9Lg 4' = Oi I1-tlnn tgar i: 4x=arctgl- nn.n-Zi x Aarctg B1 4'nFLi 5) sin':r - 5si.n r cosJ. + 6cos'r=01: cos',; tg2 ,. 5 tg' + 6=0' SaMiHa: tg, = t. t2 5t+6=Oitr=2"=3. O6epHeHa 3aMiHa: te t = 2t t = arctg 2 + nn, n e Z; lg r = 3:.r-ar.tg 3 - nh- k - Z. BiAnosiOb: ^rcte 2 + nn, n e 4 ^rctl 3 + nh' k e Z" 6) 4sin'::s- 3 sin .r cos :c - cosr :r = 0 | : cost4tg'2t-3tgt 1=O' Sevinai 1g x = l. 4i' - 3i -l 0r D - (-3)', 4. 4. (-) = 25i,1O = S; t, =?E = t; O6epEeHa aaMiHa: tgx=7; t =+ nn, n ez; 11 tgx= : .r = -arctei+ nR. n e L. .1 Bidnostdb: " -F arcLc;- nh. n' k - Z 835. 1) 6 cos't + 5sj.nx-7 =O;6(1 sin'zjl:) + 5 sin t - ?= 0; 6 - 6 sin't + 5 sin jr ?= 0; -6 sin'n + 5 sin '=0Sauinar sin;c=t. -6t'1+5t- 1=0J: (-1); 6t' - 5t + 1 = 0; D = 5' - 4 6 1=1: - 5+1 r 5 I I JD.l: il- z.t Z, t ZG t' O6epllena saMiHa: .r." = 1, r=r tt'L+nn,n.z; 2ti 11 'inx i: .t (-Irlarcsin nk AFl' '!t I t n*-n-k-7Bidnfiidb: /-7l 6',T,?: l-1) arcsLn J 446 li* AnrE6PA Mep3neKA. f. ia iH. AKaAeMi{H,r pieexr i:::iliii:ii::l:i:ili 2 2(l -cos'r)+ 7 cos t + 2=O;2 2 cosz r + 7 cos r + 2 =0; -2cos'zr+Tcosir+4=0. SaMina: cos , = t. 2t, + 7t + 4 = O I I C1; 2t, - 7t - 4 = O; D=t-lt:-4 2.{-4,=8lr vD 9: / t^'.n *' ,. t.+=-1 22 2.2 2 O6epHeHa saMiHa: cos r = 4; ftopeEiB neMa€; t, * .( ^ ***'l ,^,., z,,= ?!-2nn.n,r. 2 2) 3 Bidnosidi: !2n t 2nn- n - / - 3 3) 2cos' jf- 1- 1 - 4 cos r = 0; 2 cos' r - 4 cos x 2=O. SaMiHa: cosr= t.2t, - 4t - 2=O .2; t, 2t 1=Ot D,={ 1f - 2.(-t=2: t; t;.. ,, t;-. , t; O6epEeHa saMina: cos rc = 1+.8; nopesiB HeMae (r +.8 t r); cosr = 1 nD; x=x.arccos(t-nE)+znn,nez. Bionosidb: ! arccos(l Jz)tznn., -2. 4) 2cosr (2cos'zn- 1) cos,r=0; 2 cos, 2cos,.r+ 1-coszr=0; -3cos'zr+2cosr+1=O. SaMiHa: cos r= t. 3t'+2t+1=01:( 1);3t, 2t-1=O; D=t tl 4.3.r tr 4 rt2 t6i VD 4i i 2rtl t , O6FpHpHa 3aviua: cos x lr .:r htn. n - Zl !, ,-,( , a.ccosl'l +:n*.ecz. 3 3) Btdnosdb: 2nn, -r^ "...."1.l 21*, n, h * L. 3l 5) (1 2sin' jr)+sinr=0; 2sin,r.+sinr+ 1=0. SaMiHa: sin ir= t. 2t'+ t ).1=01i( )t 2t, - t - 1=0; D = 1 - 4.2. ( l)=9; ,6=:, t.=1-3-t' ,^ r-3 -1.' 2.2 ' 22 2 O6epEeHa BaMiHa: n,stnx= li x= +zfin,n€Li .inr= l, a=t 1tt't!+nk-kF7. 26 Bidnoaioa: L+2nn: t-It"' - nk.n.k.L. 26 er z.o"'{-r-r"n"1-2=0. BrMiE': "."1=1- 21:- 5i,3=61'333 D-l5F 4 2-3).49:.JD 7: t 5'7 " , 5 7 I " 22'"' 22 t' ooepHeHa 3aMiHa: cos{ = 3r xop.r:le '"'o,; 1, " -l " ,--"tl',',., ez, x -2^ znn.o-2. 3 2 3 2) 3 3 r=!2n+6nn-neZ- RiAnoqiAb: X2fin + 6fin, L e Z. i;i:::::ilLiilti: AITEEPA Mep3rel(A. r. ra ifl. AKaAeMi{Hr.ri piBel/.b;i,:.:i 447 2h "E- 23 3 - 3 5 _! " 2.4- 4
  • 7) 1 2sin x {l-sin'rl-J2sin'r=0r l-2srn-'r-l'sin/x Esinir=0: - sin' :r: - rE sin r = 0. SaMiEs: sin.t= r, ',t'-f2t=oj t(l+.€)=o; tl=oa6o t,=-Jt O6epEeEa saMilra: sitrl',=O:t=nn,neZi sinr = .E; rcopeEiB EeMae. BiA o6iAb: nn. n e Z. ?-- ar -"j ' [z*"'j - LJ = o, z*"'i - -"i -r = o. 3auisa: cos{=r, 2t2 +t 1=O; 2 - r-3 l'3 I D=l -4.2 f-I).9i VD 3i = 2 2 = t. t,- 2.2' 2. O6epH€ra 3aaliEa: "o"{=.1: r-=n t2ftn,nFZ; x=2n -Ann,ncZi 22 2 .".;" i, ;= -l-zn*'*.2, x a+ t ank.hez. BiAnoidb: i++ 4rki 2n+Ann.nez. 1fik 9) ter-- J-2i !t-. gx saMisa:te,=1. t+!+z=0; t'+?t+1 -0. I:':;'.t='' (,r1)z=0; r= 1. O6epdeHa 3aMiEa: tg t = 1i x=-:+fin,neZ. 16, g.1---j919{,41t cos,6x)-5=0r 4cos,6jr -4 cos6.r'3 0. 2 SaMiEa: cos 6.' = t. 4tt + 4t - 3 = Oj D - 4, - 4.4. (-3)= 64;,!o = a; t, --j:3 = -?'2.4 2' -4+8 "' 2-4 O6epEeEa satrfiEa: *"6t = -;; &opesin Her'{ae; cos6r = ! t 6, = ! arc.orf,+ zn, o. z; 6x = xI + 2nn, n e Z; ftnnt=+-+--neL. 183 Bilnoeiaa: !{j+!, nez. Irt 4tesx+-9 '7=0t 5x*T.ncz, * 'ff.r'ztsbx 2 a 4t-7t'3 - l4!" n+a o, 3aMiHa: tg5,r= t,4t +=-7 O,- ,- uilr*0, D r7l, 4.4.s-l:.lD=t, t, =.7r+r1 =rr ,"=?; i 448 !!{j AITEEPA Mep3ntK A. r. ra iH. AxaaeMi'rHlli piBeHb iillia:.:tiilllN O6epEena BaMiHa: rg5x l:5x=Inn, n-Z: x ft.-Y.nEZ: rs5r=9: sr ante3 , nh.kczt ' ru"rn!-!!.p.r. - 4 "4 5 '4 i -finnl 3 nh Eidnoaidb: _+: . afcle -|_,n,k€z. 20 5 5 -4 s 12, 7 + ctg'z t = cte t + 3t ctg, a ctgr-2=0. SaMiEa: cte r = r, t, - t - 2 = Ot t1 = 2, t,= -1. O6epHeFra saMisai clg x = 2i t,= arcctg 2 + nn, n e Zi ctgjr -li *=-!+nh.*-t. Bilnoailb: arcclg 2 + nn; -! + nh, n, k e Z. rr1 2"i1': . Acos, x -7 o; 2-llcos'rt cos- J co-+4cos-x /=0' aaMiss: cos,.r = t.?-2t,tr z=g.2-2t-tl-zt =o. [er" srtz=o' t t li*o: D ( st .4.4.2=4si lo z, r,=Lz.l ,, ,,=+=l O6epEeHa BaMisa: cosz r = 2: .osr = -!f2 a6o cosx =.Et kopesis HeMac: "os'x= l, "o"*=-1.'oo "o"'=1, ' *2!,2,,,.,--- '- 4' "" 2 --' --'^ 2' ^ a6o t=rI+2nh,heZ. Ilicnn o6'eAHaEHs ABox cepi:fr ftop€HiB oAep[ryemo t + nn, n eZ. Bidnosidb: t') t nn. n c z. 14) 2 cos' r - 1 - 4/icosr + 4 = 0; 2coe' x - 4rE cos x + 3 = 0, SaMiHa:cos'=r. 2t'- EJ2t+B=o; o = (t,lz)' - +. z . a = a; J-o =znE; , aJr-2J2 BJ2 aJ2 2,2 .tE "= zz z"'= 2.2 =T' O6epEena BaMiHa: s.[2 la,6 -)cos.r= 2 i kopenrs neMac | 2 >]J: t;-.osr = - ;: x-,".2nn.ncz. Bi'noiiAb: r! + 2fin, n eZ. 836. 1) 4sin,Jc + 8cos r + 1= 0;4(1 -cos,r)+8cosr+ 1= 0; 4 4cos,r+ 8cos r + 1=0; -4 cos, r + 8 cos, + 5= 0; 4cos'z,q 8cosr-5=0. SaMina: cosr= t. 4t, 8t - 5=0i ii1:itii:::lillil: ATTEEPA Mep3nrKA. f. ra iH. AKaAeMi{Hran piaeau !il: l5 yci rtq r0 u., !. I 449
  • T' D=r-8) 4 .4 b t44i Jo tz, r, a-.12-2.s, , =";Y= L 06epseEa saMiEa: cos r = 2,5; KopeHiB HeMae; | / l -n.2, ' =4 znn.r-2.cos -r ' - t; jf +| n - arccos 2.J I 2", s Bianoaidb: !4 +2ILn. n €2. 3 2) 2(1 sin'j9) 1 sinr=0; 2-2sir2x- 1 sint=0; -2 sin'? r - sin , + 1 = 0 I : ( 1);2sin'9t+sint 1=0 SaMiHa: sin r = t. 2t'z + t - I = Ot D=r, 4 2.{-1) 9i Jb.s: t.= )-r"=-t, ,,'}.trt I 06epnesa saMiHai srnr= 1: -r= +2nn,neZ: 26 Bidnoeiot: n,21t 1 ll' -2nh, n,k'-Z- 26 3) 1- zsin'.T + 8sin n 3 =0; 2siD't + 8sin t-2=Olt( 2); sin'zr-4sinr+1=0. SaMina: sin, = t. t' - 4t + 1 = O; a ?fi z*h, t.=z $D = 16 4 = 12: .lD 2J3t t, -2 O6epqeHa raMiHa: sin:r=2+16; ..ope'iB EeMae (z *.6 t r); sinr =2-.,6; r = ( r)"arcsin(z-16 + nn, n ez. Bianoliab: etl. arcEi"(z - nE) + "", " .2. a) (2cos'9, 1)+(1 cos' x) - cos t = 0; 2co]' x - I + 1-cos2?-cost=0j cos'r cos r= 0; cos t(cos t - 1) =0; cos r = 0, a6o cos t - 1= o; r =! +nn, neZ ' a6o x = 2Th, he z' Bidnosiab: +n 2nki n.heZ. 2 5r SsinI l, -"ll ' 2 0; 5sin 1- 2sin'1- 2 o. - """6 ' ---31 6 6 sawisa: sin{ = t. 2t'z+5t +2=Ol 6 D=5, 4.2 2 st,[D s; t,= 5.-r3 = z, t.=-f,tr3 ='t. O6epHetla BaMiEa: "in I = z: xooesls rreMae: 6 .t"* -1. ' r rf 'L nn,nez; x=( 1)' n.6nn.nrz- 6266 Bi0no6iAb: Gl"'tn+ 6nn, n eZ. 450 lii: AIrEEPA Mep3reKA. f. ra iH. AKaAeMi'{Hlafi piBeHb :::a:::::i:::::i:i$:i 6) 1 - 2sln' ; + sin; = 0; -2sin' ;+ sin; + 1 = 0; 2sin'; - sin; - 1 = 0. 3ar',rina: sinl=t. 2t'z t 1=Oi D=r 4.2.( 1)=e; 5=e: t,=!j=ttr=i:= + O6epEesa 3aMiEa: "t"|= t: |=!t2"", n.zt '=n+4nn,nez; '^ ; = - t, | = t-tl' f, t nn, n. z, r - (-:rrhi ! + 2nh, k e z. Bidnoiidb: n - ann: t-:.f 'i|- 2'th- n, k , 7. 7) 2cosz 4' e.1*?"4'*r=o; 2cos'4t 3 Scos 4ir + 1 = 0; 2cos'4r Scos 4a 2 = 0. 3aMiH€: cos 4r '. t,2t: 3t 2 0| D=(-st, 4.2.2=25,5=s; t,=f;j=zt ,=#= ;. O6epseEa sarilla; ros 4.r = 2i HoppniB HeMac: cos4.r },.- -f^ n)tzon.nez: 4x -2n 2nn.neLt x=+!+.nez. 63 Bianoaioa: tl+!, n ez. a) ter+-L a=0. SaMirla: tg jr = 1. 2 t'!-3t+2 ll gt2=o. i, 3 0: l, 0F ), l.=2il-=1. t t Ltlo: O6epHena BaMiEai tg x = 2;, = arctg 2 + nn, n e Z; tax=l: x=L+nk,keZ. Bidnoaidb: arcls 2 ' nn. ft nk,n,hFL."4 9) 6tg'+3=3(1+ts"x); lite" r '6ter=0. saMisa: ts ' = t. 3l - rf3t = 0i .far(J-:t-r)=o; r-ouoo O6epHeHa saMiHa: lgr=Oix=nn,n.Z; 1n tgx = !9; x=1+n&,keZ. Bianoliab: nnt [ + n*, n, * e z. ljll::li::tlii*: AITEEPA Mep3re( A. r. ra iH. AKaaeMi,{Hrr piBeHb ili: 451 l5* l i ,=+=@ J33
  • ror n"in'' * g{ -1- - rl -u=0, $n-.r ) 4 sina t + 9 - 9sin', - 6 sin'? t =o- 4/--15r'9 - l4l'-15i 9=0' 3aMiHa: sin, .r = t. -- - u o lt * O, r5-9 15-9 D 15,.4.4.9 8l:JD=9i,,':.n =u, t,=- - O6epEeEa sanriEa: sin'z , = 3; IcopeEiB lreMa€; "3!5"6sinz j=:: sinx= 2-.aoo srnx, tl ,. r-1-"! +nk.k.Z.a6o x=l tl -L-nn.ncz.-:li, nicns o6'€ana$ss lsox cepifi HopeHiB orpxM*'o - l-* ^', ' c z' Bidnoei t: !!+nn,neZ. 3 837. 1)sin't+ 0,5 2 sin tcos r - 2 cos';=0]|cos2 r; lg2 x+gx- Balfil:ai Lg t - t. t' + t - 2 = 0i = 1" t2= -2' O6epseEa 3aMiIIa: lgx=Ii x= +nn.neLi tgx= 2ix= arcLe2 -rtk' hF Z. Bianoaida: L t nn: -arctq 2. nk, n, h' Z. 4 2 7 sin' 5t - 4' 2sin 5.' cos 5: + cos' 5r = 0 | : cos'z, 5r; 7tg'1 5x 8l,g 5r + 1 = 0. SaMisa: tg 5x = t. 1t'z - 8t - I = 0i - i+6 8-G D=(-8)? 4 ? l=36; JD=6i tr = -r.:=lt t,= Z.Z= O6epEelta 3aMilta: tfr!.nezttg 5.'r li 5r '"-fin.nczi *=m t 111111k- tgSr ;: 5.r = arctg ; + nh' k c Zt r=tarctgi+ 5,he'' nnnllnk BiAno1idh: i'n+:b' i ;^tctc; - i' . n, k ez. 3) cos':, + 2sintcost + sir'zJc+ 1=1 2cos%c;1+ sin 2t 1+cos 2'=0: sin 2-r- cos 2.r=0 1 : cos 2-r: tg 2n - I =0: tg 2t -li 2x _! + nn, n.zt x=-;+;,ncz: 41 3sin'z.t- Tsinxcosr- l4cos'x 2(cos'? r + sinT r) = 0; sin!x - ?sin.r cosr I l2cosz r=0l: cos, xl tg'zx - Tlgx 12=O. SaMisa: tg , = t, t' - 7t + 12 = Di t'= 3t t2= 4. O6epEeEa BsMirra: Lg, = 3i x = ^rcfg 3 + nn, n e Zi tg x = 4t t = arcl,g 4 + |Ek, h e Z. Bilnosi'b: stclg A + TLni arctg 4 + rht n, h a Z' 5) 5cos'zt - 3sin'zt - 2sin.:c cos t - 2(sin'r + cos'zt) = 0i -5sinz.r - 2sin r cos.r + Scos'x = 0l i (-cos'zrrt te'E + 2te r- 3=o' Sauiua: tg x = t.'t'z+21-3- 0i 452 lll; anrEEPA Mep3rqKA. r. ra iH. AKaAeMiqHri piBet" llllii:ill:l;ili:1 D=2, 4.b.( 3)-64: Ja=6; 1,=-?:!=-l: r. -l+-q=q 2.5 ' 2.5 5 O6epHeEa BaMiEe: ts x = -1i 1= -Lana. a 12.-4 tgx =::i x = arctg:- + ftk, k €2. Bidnosidh: -L + ttn: arcte 3 t nk. n. & e l.4 '5 6) Ssin'.' + sin.I cos r + 4cos? r - 3(sin, r + cos, r) - 0; sin r cos. + cos2 r = 0j cos r(sin r + cos x) = 0; coat-o: x=!+nn.nez: 2 a6o sin x + cos , = 0 : cos r; tg r + 1 = 0; tg r = -1; BiOnosiab: ! + nn: -! + nh. n. h ez. 24 7) &in, cos r + cos? r - (sin'?, + cos' r) = 0; 3sinrcosr-sin2r=0; -sill r(sin r - 3cos r) = 0; sir']c=Oix=rol,neZ: a6osinr-- 3 cosr=0 : cosx; tgr 3=0; tgt=3; t=atctgB+fik,hE Z. Bidnoaidb: ftni arcLg 3 - fih. n.he Z. gt 2cosr + sin x _ 1. Tstnx - cosx 2 OA3: ?sin r cos r * 0 ] : cos r; |tg t - f + O; tgz+f,: 2(2cos r + sin,')= Tsin i. cost; -bsin r + 5cosr=01: n_tgx=ri.x= +tt4n€L. 838. 1) sin'z, - 2 . 2sin t co_s r + 3 cos' x - 0 | i cos2 $ Ng2 t - 4trg t + 3 = O. BaMiE&: tg r = t. t, - 4t + A = Oi t1= 1t t2- 3, O6epEesa BaMiEa: tsy=l; y=!qnn.rg7 4 tg t = 3; r = arctg 3 + nk, h € Z. Bidnoiidb: !-fin, arcta3a n*. n,n h- 2. 4- 2) 5sin'? r - Ssin r cos r + 2cos, r - (sint r + cos, r) = 0; 4sin'zr... 5sin, cosr +cos3r=0 | cos, t;41g, t- Stgr+ 1=0. SaMina: tg r= r. 4t'-5t +l=O; D = (-S), 4.4.1=9t ,6 r, ,. 5*1=r, r =!--q=!.' 2.4 ', 2.4 4 O6epEeEa saMiEa; 1t_1gx=ri x= +ftn.neLl 5n, = !.. , = *.1n!*np.1r.7.- 4 '4 Bidnoeidu: +rn: arcteL - rik. n. k.:2. 4 -4 ilililli_tl:j:.tt A'lTEEPA Mep3rrKA. r. ra iB. AKaAeMi,{Hri piBeHb l:it x=-!+nh.keZ. 4 2=0. x*ar*ef,+nn,nez; (-5cosr);tgr-1=0; l 453
  • 3)6sin2r 2 2sinrcost l4cos?r. 3(sinz 'r 'cosr.rl=0: Bsin,.r+4sin 0l:co'.r:3tg x-4tex -1=0. SaMiHa: tg r. l. 31': ' 4/ . I 0i - 4-2 I -4-2 D 4, - 4 . 3 . 1 = 4t ,l D = 2: t,=-2.3 =-Ji rr= zB= r. O6epEeEa saMiEa: rltg.x = -Fi .{=-arcigg+n,neL: tsr= 1: r= +nk.hez. '4 1JI Bidnosidb: -arctg;r ni -;- rk'n.k -7. 4) 2cosz t + zsin r cos ir 2(sin' t + cos': t) = 0i 2sin'?t+ 2sin T cos.I=0; 2sin n(sin x - cos .T) = 0; sinr=0: r=rz, ne Z, a6o siLt lc cost=0 : cos]'; tg, 1= 0i tgt=1; r =! +nk- h eZ. 4 Bianolilb: nn ! + nh, n. h eZ. 4 5) 3sin'.r 2."6 sin:r: cos t + 5 cos'z t 2(sin'z r + cos'? t) = 0; sin'x-2J3sinx.os-r, 3eos'x 0l:cos'r: !e r 2'6rer'3=o: {re'-Jr]' 0: rer 6=0r ugx=J3r x--f, tnn n't' 6) 2 slan ig!1 l; o.[3: rsin x 4cos.r' 0 : cos'i srs.r 4 /0: 5 sin.r - 4cosx 3 x+acctel-nn,ncZ: 3(2$n r cos x) ssin t- 4cos x: 6sin x Scos r- ssin x I 4'os x - Oi sinr .os r. o:cosxilg.t,l 0:tsx -r., -It nn,n -Z' 839. (1 - cos't) + cos, + 1= 0; cose, + cos jr + 2 =0; cosz t - cbs t + 2 =0' Sa]IiEa: cos t = t. t2 t - 2 = O: t.= 2" t,= -1. O6epseta 3aMiHa: cos t = 2; (opesiB HeMae; cos x = 1; x=-It+fin,nEZ' flpu n = O: z = r - Hafi6i"tbrrt{i BiA'eMsnft lropiH6. BiAnMiA': -n. 84O. sin'zir + 0,5 2sin n cos, - (sin'z.' + cos'zr) = 0; sin.!cos n- cost r = 0; cos t(sin t - cos ,) = 0; cosr=O: r=I+nn,neZ'2 a6o sin r - cos x = 0 I : cos t; tgt-1=0;tgt=1; x=+nk'keZ' '= t, "= n=-?!. tr - uan6i,rsmrs Bi,q cM$Hii KopiH6. 2 Brdnoaidt: -L.2 454 li:i: AITEEPA Mep3rqKa. r. ra iH. aKaAeMiqflr,ti piBet" iliillli:i;i;iiiil: a41,61 c9s2{ +2(1 cos:2.r)=5;3 8cos2r+2 2cos'u 5=o; -2cos'x - Scos 2,. = 0; -cos 2r(2cos.r + 3) = 0; cos 2t = o; 2:r=Z+nn,nez; x=f,+!,nez: a6o 2cos jr 3 0r *"' - - t: KopFHiB HeMac. npun=o:,=x. Bilnoai}t: !. ,4 842. cos t(sin jr + cos ,) = 0; cosx=o) x=L+nn,neZ; a6o sin iu + cos r = O : cos r; tg x + 1 = 0; tg r = -1; x=-!+nh,keZ. npvn-o x=i, net4k=o x=-|., opx*=r r.= -X.^=+ Bidnociab: !. 2 a4s. r) 2sin2.r :::;-ff;, x .nlt zsinzx=":"J,";";*, 2,in2, = -L. ,in' 2, = 11 sin 2x sin2.r=-1: 2x= !tnn,neZ:, n rnn,n-z:242 a6osin2x l: 2x n ,nh.keZ: t n rnk.k.2.242 Bidnoaida: ! +9- n e7.. 42 2) 3 cos,r . '"t- o, oflt, cos,r*0i,rF n -an,ncz: 3..s'? x + 2sin r 0; 3(l sin:.r) 2sin -r 0; 3sin'z-r l2sinx r3 0; a"in'.lo"i.in , r o. BaMisa: sinr=r.3t, 2t 3=OtDt=( 1)? 3.( 3)=10; ,,;'i; .lE ="To. r.=l '/ru. r^=r vro. O6epEeHa aaMiHal . 1+ J1o nopeErB HeMac: r-.,/io 1 ,R _n,,,.2.gnr= e l ir={-r) ar$rn ! Btd,oetabi (-r)" arcsi nt f; *no,n.z. ::li:al:il:ilil:l AITEEPA Mep3rrK A. r. ra iH. AKaaeMiqHrn piBeHb :ii::; 455 4 tg +;;
  • 4cost 2t 4cos 2x - 3 = O. SaMiEa: cos 2t = t. 4t' - 4t - 3 = O) D = (-4r, - 4. 4. (-s) = 64; JD = s; er g. l - cos2x -4r1 cos'2.r) rScoszx-5=oi t - tcoe 2i + I - 4cos' 2t + Scos 2x 5 = Oi 4cos2 2r + 4cos 2t + 3 = 0 L : (-1); 4-A 1 ' 2.4 2 O6epseEa 3arriEa: "n"2r = 9: Kopenin seMae; 2' r ( r) 2ft - "o.Z'=-i, 2r-+f tr - arccos;J |21tn,n'Zi 2x'Ia-znn.ncLi - 'i,"^.".2. Bianosiab: !;+ nn, n ez. 4) 3 + scos t = -(cos' .t - sin' .'xcos'z t + sin',); 3 + Scos .' = -(2cos': r - 1); 2cos"+5coB.r+2-0. gaMisa: cos, = t. 2t' + 5t + 2 = Oi - -5.3 -5t3 I D=b,-4.2.2=9..ID-3t = ;.2 -4: I, z-2 =-t. O6epnesa BaMiEa: cos r = 4! RopeEiB seMa€; e loo (o l;6 ) "o"'='S ixopeEiBHeMa€ l. 'r"". -',]. aidnoaiab: xarccos@ 2 + 2nn- n e7.. 5 2) 4(t - cos'2x) -7 co.2' -2.r-':"2' 6l'2 4 - 4coE'2x + 7cos 2x - 1+ cos 2.rc 6 = 0; 4cos,2l + Scos 2r - 3 = 0; 4cos' 2r Scos 2r + 3 = 0. 3anIiIIa: cos 2, = t. 4t' 8t + 3 = 0i D.t at' 4 4 3 r6i ,to +; t,- l!=3;: t,= 2.4 2 ' O6epHeHa saMiEa: 3 l: 2t=L!+2nn.nL7.:.oszr = 'i xopeHrs ncva€i co32.r ' 2 3 t=!!+nn,neZ. Bk)nosiAb: lL + nn. n e7.. 6 s) 7+2sin2.r-r,5rgl--':""1 - o; oaa: t, n!,n ez; cos.r srn -rl 2 ?+2sr2r+l'5{sin'zr' cos'r) 2 =ot z v 2sin2r r 3- =0,cos.r sin.r 2 sin2x zsin'z2x+7sn2x+3 "i =0t 2sin:2r' + Tsin 2t -3=0' SaMiHai sin 2, = t. 2t' + 7t + 3 = 0i D ='I' - 4. 2. 3 = 25: Jo 5,,. _7_5 g, 1"__!:J=_!.' 2.2 ' 2.2 2 O6epEena BaMiHa: sin 2, = -3; (opeHiB seMae; sin2x - 12t 2x 1 lfrarcsin I I nn,nei 2x = t-l"| ! + nn, n c Z: a = 1-11"t !: a!. r 62. 122 Bionoaiat Gr)"' $+ !, n e z. ar sin.x=lcos,r-st".if".",-, "i",r), "i".,=.*,. r, 22J22) (1 - cos'zr) cos r=0; cos?r- cosr + 1=0i cos'!r + cos r - 1= 0. EaMina: cos r = l. t' + t - I = O', D = l'z - 4 1 . (-1) = 5; -E=s, ,.= 1 6, r --r+n6-'2'2 O6epEeFa 3aMirra: -r-.,6 (.r Js -lcosir 2 i ropeHrs seMac | 2 <-r.]: cosx . Vbj-I. r = larccosJ - 2nn, n cz. BiDnoaiu: t arccoe@| + 2nn, tu e z. ilillliii:ltlll AnTEEPA Mep3rrx A. r. ra ir. AKa.qeMi{Hratr piBeHb lil: 4+8 3 8-4 I 2.4 2 $sd ll:liI ffi l 1 I 1 cosx -t; r =-Lln-arccos;J+2rn' r ezi 2n Bidnoqidb: t-+zftn,neL I - cos.r 5) 2cos'.r-1 gcosx+6=4 -.- i r=!?+zrn,nez. 7 -5 |.,42 ne Z- 2cos2 t - ! - gcos t + 6 - 2 + 2cos t = Ot 2coB2 x - Tcos t + 3 = 0' SaMina: cos :r= t. 2tt 7t+3-O: D=(-7,--4.2.s=25: JD -5; t,=1!-s; O6epEeEa 3aMilra: cos , = 3; &opesiB EeMae; s6gy=; t = +!+ 2nn,n ez. BiAnosiab: t:I+ 2nn, n eZ. 844. 1) lPa-ssin'=0; o,43: sin'+oir+nn, 4cosx-ssin'/n-0. n:gSlj!L-g:14 o: 5cos,.r - 4.osx s=0. cin r srn,f, SaMisa: cos t = t. t'z + 4t - 5 - Ol D=2, s. (-b, = 2s; Jo = Jm; O=-'*u@ , O6epaeua saruina: -Dt,l2s fi 2.znn,nrz,cosx = - ;-; jr = larccos-- 456 ii{: arrEEPA Mep3rex A. r. ra iH. aKaaeMiqHrlr piBexu fflJliii:iirif$ -2 Jn 457
  • b 2 (2cos' 21 1)-2.1119q?1-scos2x-0' 4cos'2x 2-l cos 2t - Scos 2x = O; 4cost 2t 4cos 2x 3=O' BaMiIla: cos 2, = r. 4t, - 4t 3=OtD=(-4), 4.4. ( 3)=64; Jr=S; 4+8 3 4 8 1 t,= z.a=ir t,= 2.4=-t' 06epEeHa saMisa: "o"zr = ]; ,,on""ru *"-."; "."r-- l, * -("-;) ,2,.n.n-Li 2,= t2[ +znn'n-2. r=+L+nn.neZ- 3 Bilno'iab: !:+ nn, t eZ. 845. CtoprcraeMoce roroxisocrsMlr: "in" = z"n1.o"!r; co"' = "oJ f, - "in'I " l- rl ".*'r-, "t,,'t'l = o:trazsinlmsi-slcos';-stn'?;, 2 z.) 6"i";cos; - s"oJ ; + I sin" ; - s cos" ; - ssi^" ; = 0; ssin' f, + osinlcos j - 11cos'z { = 0 t cos' }; s tc" ! + awf, - n = o. 3,amisa: tg! = t. 5t' + 6t 11=OtD=6'z-4 5'(-11)=256; . -6 t6 ll -6t16 - J, 16: i. 2.5 5 , i, 2.5 , O6epEeEa saMisa: t*;= T,r=-""(--'Jl ,^n.n-zi x= zar"tslt tnn.n-7: LgI r. {= | tnh.k.z.. ,=!,zn*,*,2--2 2 4 2 Bionoaidt: -2arc4! nn., cz; |-zn*.n.t,z t .x ,ir' .r 'l ^2t 2zsin;aos;s[.os't sin;J tl."."', sin tJ u: 4,n;."";- 8""{ ;+ bsi.';- 3co{;-ss,";= o' -scoJ j+asi"]*"{ + z"in" ! = ol.z"os" X: te"}+ztc} a'=o- 3ar'dua: tgI=6. t'+2t-4=o;Dt=1' l'(-41=5; t' =-1-G; 4=-1+J5 O6epEe:ra 3alttilla: tei--t Js, i= *.tc(t nE)+nn'nez; x = 2arctg( t-'fi)+2nn,nez; w | = t +,li; !, = *.tg( t t Ji + nk, n e z; z = 2 arcts(-1 + Ji) + nh, h e z' Bionoliab: 2arc].1g(-l n[E) + znn, , ez. 458 iriaAIIEEPA Mep3rrx a. r. ra iH. AKaaeMieHrar pieenu llill{f:i:ilf:ii 846. lt 3 2sinxcosr,sl-"'* .i"''), sl-. {,"; {J =o,2l 2 2) 6"i"1"o"{ 15 "o"'{ - 5sin'3 + 3 cos'{ + 3sin'{ = 0: 222222 2sin'x , Gsrnrcosr rscos'r 0l:f 2"."'Il, tn'{-:rL'x-a o. 2 2 2 2 ! 2l '2 '2 SaMiHa: LC; - t. t2 3t 4 Oi tt 4i t, l. O6epEeHa BaMiHa: ugl=4; {=u."t*o- ftn.n.li r 2arcle4 | 2n, n .Z;'2 2 rn{= .1, I=-I1nh-k,-Z: x.-n +2nh.keZ.'2 2 4 2 Bidno'idh: 2arere4 r 2nnt n t2nh,n,hcl.-2 2r sJa 2sinlcos{-sl-"'.'-"r"'*l z["."'' "r"'') o, 2 2 I 2 2' 2 2' . ,x _ ,tt)/J srn cos 5.os--I5srn---/cos' - lsrn- tl: 222222 -2":. r+0,,6"i"i"*i-t2""*i ot,( z*' l); te'|.a,E"sf,+a-o. samina: rg{=i. i'-e,fit+o=0, D (3J3)' a.6 27 2a=31 uln =,f5.2 -t; t; ^t; t; r ovo vo l;-. ovo-vd o/o '2-2 O6epIIeEa 3aMiIIa: 1s I = u/3, {=Iann,ntz: x=zn,2nn,nezi"2 2 3 3 t* t = ""Et | = arcte 2rE + nk. k e z: x = 2 arcte 2Jz + 2nk, k e z. Bionoeidd: "l' - 2an; 2ar.cte2E | 2h, n, h t Z. 3" 447-l)l 2sit]''r+ sin r= (1 sin,r)=0; I - 2sin, r + sin r 1+ sin?r=0; sin':, + sin r=0; sin r(sin r - 1)=0; sin.r=0:x=nn.nc Z: a6osin x I 0isin ,-1, *=!-2np,k.2. Ilpr.rn=0:r=0; npun=1x=n; npBn=-1 .r=-7r:npx k=O x=*: e= 1: r 3r ixo*: npxk=t *=l-zn.5] "-. "*ou,'" x= 2-2fi - 2 se BxoArl,rr, ] Dpov 2 2 y rpoMidioK. Bidno6idb: 4 KopFHi. 448. 1) 2(1 cos'a) + Tcos.r + 2 = Ot2-2coE':t+Icosr+2=Oi -zcos: r + Tcos r + 4 = O I : ( r). SaMiHa: cos .r = i. 2t" 7t 4 OiD ( 7), 4 2 e1f,=81;,lD gi , 7+9 ,. , 7 I 1 ' 2.2 2.2 2 O6epEeEa 3aMiHa: cos r = 4; rcopeHiB EeMae; :iiiiiiitiii:i* AITEEPA Mep3rrKA. r. ra iH. AKaaeMi{Hhr piBeHb l:::t' 459 I I
  • 12n +2nn-nEZ. -2T-2^2nIlpr a 0 x =-:-e6o r , ,-? t" Bxoal'rrb y npoMixcoft); nvttn=t ,=-!+2,=! ,e" r=f *z*=$ t"".xoa,'rr, y rpoMixox); 2ft 4n 33 Bi.Ano6iAb: 2n. 849.2(1 - sin't)=sin x; -2 sin'jr sin;r + 2 =01: ( 1);2sii'zt + sin t - 2 =0 gaMina: sin , = ,. 2t' + t - 2 = Oi D = 1 4'2 (-2)= 17i t -,hz- I'Jlz u[7 t vr'vrii rr=-4 : t,= Z.Z 4 . O6epFeHa saMiHa: r Jrz (-ttJtt .)sinr.= 4 i xopeHr! Eex,ra€ I a-.-t.], "r,',='r;-t, :q = Gr)" *"sin@l +M,nezi li;., urlr n = 0 r = arcsin gil < jr rrpr n = 1 lr = - arcsi n[', t * n. ^ ,47-r 4 aso. z"i"l*"i**"'r "i''i--"'i "i"'i -0, -2"i""!+zs'"t."'i=o; "i"|= o; |= nn, n ezi r-2nn,nez, aoo sin j -cosf, = o l, "o"|; tef, -t = o; 452. 1) cos" cos r + a - .r2 =.O. 3aMirra: cos r - t. t' t + a(1 a = 0, [t.+t-=1. 3a reoppMoro Bi.ra I tt ai tz I a. li, .i. = o0 _ a): PiBssHHs MarnMe KopeHi, sKqo -1 < a < 1 a6o -1<l - a<1; -2 <-a<0; O< a<2- BiAnoqiAb:-1sa<2. 2) Eijn'r- 2aEiI r+ 2a2 4a + 4- O. gal'riEa: sin r = ,. t' 2at + 2a' 4a + 4 = 0t D,=( a)' (2a, 4a+4)= a'+4a 4= (a' 4o+4)= (a 2),, PiBIIsErifi Ma€ &opin6, snqo ,r > 0, BiAnoqiAb: 851. 1) sin'z .is (34 - 3) sin , + a(24 - 3) = 0 SaMiEa: sin r = t. t' - (3a - Aft + 4(2a - A') = O. li +r.=r, 3a reopeMoo Bj€ra I ' ' l,= a - 3i t" a. ' 1, t'=a(r-a): PiBEsgns MarrM€ Kopelri, triDro -1 < 2a - 3 < 1 a6o -1 < a < 1| 2 < 2a < 4i 1 < a < 2. BiAnosiAb: 1 < a < 2. 2) cos" + 2 cos r + o'z - 6a+ 10 =0 SaMiEa: cos r = ,. t2 + 2a + az 60 + 10 = 0; D,= l a" + 6a - 10 - -la' - 6a + 9 = -la - 3)'' PiBHfisBs Ma€ Hopilrr', axqo ,r > 0. -(a-3)z>0trpra=3. fipna=3t'+ 2t + l=0;(t + 1)'9= 0; ,= 1, pinng:rHs Ma€ xopiHl'. BiAnosiAb: a = 3. 460 i:::i: ufespl Mep3nrk A. r. ra iH. AKaaeMiqHul pisexu :i:li:ii'i:ili:i'.;i:: :(a-2r'>-0IJp]'a=2. S{o a = 2, t' - 4t + 4 = Ot (t - 2r' = 0; t = 2, npore sin r = f, roAi sin, = 2. PiB' IIsnIIs nopeHiB Ee Ma€. BiAno'iAb: aalrorc BE '{eIIEs a IIe icHy€. ss3.r) rVZ t'{tz; '{n,,{Ez, *o*v iF ''V77; 2) Jz i ,V33r 'F i ,Vra, ,V42.'V33, 'o..v Jz. t,fra: st fr# i i6rr 9225,a!t2s, 'ouy Vts 'vs, al {F i {6; '{tr ''iF, ,o*v iEr ' i6. 854. r)6r(1 2(x ' 2 o: ,r = 0 a6o r 2=0; xz=2 a6o x + 2=O; rx=-2, BiA MiAb: -2i q 2. 2) x,(x - 5, + e(x - 5) = 0; (' - 5)(,, + e) = 0; ,r 5-0; ,r- 5a6o.r'z I I - 0; KopeHiB HeMa.. BiAnosidb:5- 3 ta(E + 2 + 8(r + 2) - 0; (r + 2)(r' + 8) = 0; xt2 0',x 2a6o.r{ t8 0l xopeniB Hevac. BidnoBidh: -2. 4 (it3 - 1 - (2x'z - 2t) = 0; (r - lX/ + r + 1) - 2r(r - 1) = 0; (r-lxr'?+r+1-2,')=Oi .r - I =0:.r = 1 a6o.r' - x + 1 = 0i KopeHis H"Mac. BiAnosiAb: L 855. Kirrbrlicrb % Itinbriicrf, Eilieflo I 6Dvxr 5 0,05x r II 6Dvxr 40 0,4u r CwiItr 140 r 30 42i Hexafi .f, r 6pyxry I BrAy, y r 6pyxry II BnAy. BMicr Hircenro B rrx - 0,05r r ra 0,4v r Bi,qtroBi,qEo. vcboro 6p]'xry aBox Br{aig trorpi6so Bs.Err (, + y) r, a6o 140 r. I piBnEEHs cncreMn: r + u = 140. ycLoro Hi&enb B 6pyxri ABox ErIAiB (0,05r + 0,4y) r, a6o 41 r. II piBEflEEn cscreMr.r: 0,O5t + 0,4v = 42, l,+y=1as. ]r-o.al J-0. ax - o. ae = -ro. )o.Os' . o.ay +zr lo.ob-r I 0,4y 42t 0,35' = -14: t: = 10i r + u = l{Oi a = 1OO- BiAnoaiAb: 40 a i 100 r. illiftllttiilL AIrEEPA Mep3re(A. r. ra iH. AKaaeMi'{Hrfi pigexu iii:j l6t rl x rlzsrn lsrn- - cos 2 2 2) =0; i |=f,r "*, *.2; x=L+2rh,kez. L 2
  • 6. Po3a'g3yBaHHq rplroHoMerptqHtx piaHtHb MeroAoM po3KnaaaHHt HA MHOXH}IK}I 856, 1) 2cos 2, cos ,. = 0; cos 2, = 0; 2x=!+nn,neZ: ,=+T, r.z; a6o cos , - o; x=!+2nk,heZ. Btdnoeioa: I r "i, i-n*.,.a-2. 2) 2sin 2.r.os 31 0. sin 2r = 0; ht=nn, ne Z; r =Y, n eZ; a6ocos3"r=o: 3x l+ nk. h-z:' -I-# r', Bianoaida: Y: L +4. n. * ez. 263 3) sin ,(2cos 2t - 1, + (zcos 2, 1) = 0; (2cos 2t - lxsin ,r + 1) = 0; 2rosr I 0i cos2x=!r 2x t+2nn.n.Z: ,='[ "".".2, a6osinr.,l =0: sin,r t,x= 1 2n*.kcz. Bilnoaisa: x[+ nn: :+ znk, n, k.z. ay z sin r (tg r + ,6) - (te, n J3) = o; (tg"+.,6)(2"i""-r)=o; ig'+16=o; tgx. = -',8; x=-+nn,nez; a6o2sinx r=o: "lnr lr x=t :':'in' nk,kLz. Bidnoeiat: -!+ nn; (-:ohI+ nh, n, h 62. 857. I ) 2sin 4r cos 3,r = 0; sin 4r = 0; 4r=nr, neZ; x=!, n eZ; a6o.ros ax 0i 3x=!tnh.kt7: "=i *!,*.2 ^finfifikBlonoanb: -i 2) -2sin 4t sin 5.t = 0; si:n4;,=O)4x=nn,neZ: x =Y, neZ; a6o sin br = 0; 5' = nk, k e Z; , = ! , n . Z. Bidnoeidt: !: 4. n. k ez. 45 3) is''(is' + 1) 2(te'+1)=0; (te' z - 2r(te t + tl = ol (te' -.8)(te"..,D)rtsir + 1) = o; rgr-E=o; tgt=J5; x = ardgE + nn, n ez) 462 ii!: AnTEEPA Mep3neKA. r. ra iH. AKaAeMi.rHr4i piBet" iililililiii:iii A60 te;t+,tE =o; ts,=-Jt; r=-arctglE+nk,keZ; s6otgt+1=0; tg t = -1; , = -!+ n*, ^ eZ. BiAnosiAb: l:^rclgE + nn; !+nm,n,meZ, a) .E cosr(cte,. - 3) + (ctsx - 3) = o; lctgr-:1(.ifcosr+r)=o; cNg t 3=Oictg t= 3j r=arcctg 3 +nn, ne Zi a6o .Ecos:r + 1= 0; "o"=-f, '=t(^.X)*",u,o.t, t -3n . 2o*, a. 1. Bianosidb: arcts 3 + nn: t! + 2nk, n, h ez. a5a. 1) 2coslcosr= t: z @cosr=I; "o"r=$, x=!X+2nn,nez; 2) 2sinrcosl=1; z f sin.:c=1; '6sinr=1; "*,=;t "t",=f, ir { f}'arcsin Ji , nn, n -2. *-l'-.,,1 ,, *(" . n"l 3lsinb-r sinl; r'l o;zsin 3 cos---=o: z"r.f 9" - ll "..1 l * ll = o. 2 4) .2 4) . /9-" r) - 9x n - 9r n n 2nn srnl2-AJ =u; ---=nn,n.L: 2 4- nn.ncLi x 18 -,ncLi a6o cosl *,nl o,'.I=!.nk.h.Z: !=L-! -np.1112 2 4) 2 4 2 2 2 4 ! = + n*. * ez: :c = ! + 2nh. k eZ. 242 -n2nnn'ttronostob: 1g+ Ii +zltl?,n,heL, ar "mro, "i"[] z") =o; z"in ,"'"(.,-;) "."(,,.' ;) =., (n Iz 2 t""" tor+11 2al 2 ) 2 =0; . (^ n) ^ ^ rr - - ^s'nf o.r-4.J =u: ox- 4 nn-n. Li rrx 4) nn,n-L: x=-+-,n.(/i aoo cosf+r ,n) o, a,tno=,nu.o.t, a*=|-! anp-a.71 4.r " tnk.kcTi x " t"".k=2. 4 16 4 - nnnnnkBi.Jno6idb: -+-r :-: -n.k.Z.246164 ljillii:.i{ilf;:;; mreSPA Mep3reK A. r. ra iH. AkaAeMi.rHr4i piBeHb iii: 463 10, -
  • 459. rrzs,"fcos(, ff)-', , ]*"('-iJ='' -"('-#)='' x f;= znn, oez; t=!:+2nn,nez: :r "r^l 1-s*l rsini.r 0: z"i.,lr-'l"o"ln r'l .0, ' 2 ) 4 .r 4 l "-(l l=0,"''('-l) =0, x n.nn.ncz: *=ltnn.n-z: .u" *"(; ,,) =0, *"(*-l) ='' rz !-!+nk,hez; 4x =4 + nk, k e z:, =#-*, u.t. aidnoaida: ! + nn: ff'I!,,,*.2. 860. 1) 2sin, cos r + 2sin r - (cos t + 1) = 0; 2sin r(cos t + 1) - (cos, + 1) = 0; (2sinx-lxcost+1)=0; 2sinx-1=o; "i""=]' '=CU"fi +nn, €zi a6o cos r + 1 = 0j cos t = ti r = fi + 2rtk, h e Z- Bianosiab: el"X+ nnt it+2nh,hez. 2 2cos' 4x - cos 4t = 0; cos 4t(2cos 4t - 1) = 0; , cos 4x = 0i 4t=L+nn,neZ; r=!a!!,neZ; a6o 2cos4' r=o' "o"ar= j, 4x=t:+2nk,hez; "=xft*!,n.2. Bidnoaida: "+Y: tL tI!,n.eez. 3) 2cos r cos r + cos 2t = O' c$ 2t(2.os x + l, = Ol cos 2.r =o; 2t = + nn, n ez;, = f, +, n ez; a6o 2cos r + 1- o, -", = - j' * = t(" - ;) * r^0. *. z; x = x2] + 2nk. k e z. aio,o.ia,, lt!; x! + znn, n, * ez. 4) 2sil:. 2x - zsin r sir 2, = 0; 2sin 2r(1 - sin .jr) = 0i si.' 2x = oi zt = nn, ne z; r=!, nezl a6o 1 - sin r = O; sin, = 1; a = L a 2nP, P.7. BianosiAb: T, n EZ. 5) 2sin 2r sin(-r) + sin t = 0; sin r(2sin 2, + 1) = 0; si'rx=Oit=nn,neZi a6ozsin2t+1=0; "i"2, = -f,t 2r=( r.]+nh,hez; x=ttl'fi+!,nez. Biotuoliab: nnt (-1rr ++5, n, ne z. 464 iial AITEEPA Mep3nrx a. r. ra iH. aKaaeMi.rHr4t piBenb tllli:tlJJlii$ 61 2sin2xcos2x+21+cos2x-l -0i 2sin 2-r cos 2x I I cos2x- 1=oi 2 .os 2-r(2sin 2r I l) 0i cos 2* = o; 2r = ! + nn, n ez: x = L +I!, n €2, a6o2sin2x+1=0; sin2x=-1: 2x = l-|t'-t ! - nk. k c z. x=t-lt''t n tnh.k.2.2 6 12 2' Bidnoeido: ! r $r 1 ry' ' ! r!, o, u. z. 42 122 7) -2sin 2t Ein(-r) = Ssine t; sin t cos .t sin .t - 3sin'2.f, = 0; sin': .r(4cos .r - 3) = 0: sittr=Oix=nn,neZl a6o4cos.r-3=0: "o"* = 9, *=tu'""osB + nh. k eZ. 44 Bidnosidb: nni 1*""o"1 , fih.n.heL. 4 8) (sin r + sin 3r) + (sin 2r + sin 4r) = 0; zsir. 2t cos x + 2sir 3r cos r = 0; 2cos x(sin 2.ir - sin 3r) = 0: zcosr.zsinfco"{ = o: cos -r _o: -r ' n +nn.nezl "0. "ln 1I = o, 5{ - op. a. r, , -2nh2 2 < 'R'Li a6o cos;=o; f,=!+n*,^ez; r.=n+2nm,n. z. Bidnoaida: t nn: 4; n + 2rtln, n, h, m e z. 25 9) (cos 7r - cos 3r) + (sin 8r + sin 2r) = 0; 2sin 2r sin 5re + 2sin 5r cos 3n = 0; 2sin 5r(cos 3r sin 2r) = 0; z"i"s'l"i"l n-a*l-","2;l -o: 2sinsx 2sinl n 5*l"o"l n 'J=o, 12 t4 2t 4 2l sin 5t = O) 5x=nn, ne Z: x =!!, n eZ; .6. "i"l!r-rl =0, E!-!=n*.xcz, !!=!-np.1,.y, 2 4) 2 4 2 4 fl2fik-- + .keLi 105 -lxnl- xnn-x3naoo cosft-aJ=u; 2-a= i+tin, ncL, t= -+n^. ^.zt 3n x=-+nmtnez, n 2nh 3n Bidno6'db: ;'i;o---'t -;' - nm, n. h, n -2. 10) Jfsin2.r-2sin?'sin(-2r)-O; Jf sin2,r+ 2sin7rsin2.r = 0; sin 2r ('6 + 2 sin 7:c) = o; si 2t; Ot 2x = nn, n e Z; x=Y,n eZ: :i!f!i.:iilli:i:il:.:: uresPA Mep3rrKA, r. ra iH. AKaAeMieHrli piBeHb f.i:J 465
  • L a6o 2sin?i+ J3 =0t sin?x= -;; 7x = (-lt'i ! + nh, k eZ', x=( 1t*L+!!.h€2.21 7 Bidnoaida: "": r It' " "".n.kcZ. 221 7 861- 1) 2sin r cos, + 2sin r= 0; 2sin r(cos a + 1) = 0; sint=O;x=nn,n.Zi a6ocosr+ 1 =0; cosr= li t = n+ 2nk, k e z. BiAnoqiAb:nn,neZ. 2) 2sinrcos, cos,-(2sinr- 1)=0; cos r(2sin.r - 1)-(2sin:, 1)=0; (2sin r 1)(co3r 1)=0; 2sinx I o; ";,'r- 1; r=1-l;"+nn,ncz; 26 a6o cos x - 1 = 0; cos r = l; r = znk, h e Z. Bidnosidb: l-1l L + nn. 2nk. n. k . Z. ti 3) 2sin':4r sin 4jr = 0; sin 4r(2sin, 1) - 0; sin4r o; 4r nn,n z;x f,!,n.t; 4 a6o 2sin,y I 0: sin,r .1: r=t-1f !+nk.hcZ. 26 Bianoair Y. t-ltt + lth. n. h € 7.. 46 4) 2sin 3jr cos r + cos r = O; cos jr(2sin 3r + 1) = 0; cosx O:,r fr tnn.ncz: 2 a6o 2sin 3x I 0i sin3r -': 3r -r-ll'r'' -nh-n-kc7- i=t-lr' t:-+':!.k-7- 26183 Bidnoeido: !-nn t l)^'l "'1.a.F=Z 2183 5) sin x + sin 3r + sir 2r = 0; 2sin 2r cos, + sir 2r = 0; sin2r(2cosr+1)=0; sin 2x = 0,2x = nn, n. Z; x=!,n -Z:2 a6o2cos,r r 1 0: cosx l. t -2n ,2nh.hcL. 23 R'an^Aiah !!!. +!!+2nh n he7 6) 2sin 8-r sin.r 2sin2.rsinx 0: 2sin.r(sin 8r - sin 2"r)=0: 2sin , . 2sin 5r. cos 3a = 0; sinr=Oir=nn,neZ; a6o sin 5x 0; 5x nh, k eZ, t n! , o, ,, 5 a6ocos3x 0: 3x fr -nm.ncz: t"n-nt.^.2. 263 Bidnosidb: fini !' t !' , !" . n. P. rn.2. 563 466 !i::i A'TEEPA Mep3riK A. r. ra iH. AKaAeMi.{Hrr piee}ts 'tiil:iiiii:lii:i:i 7) (sin r + sin 5r) + (sin 8jr sin 2js); 2sin 3:r cos 2r + 2sin 3r cos 5r = 0; 2sin 3x(cos 2, + cos 5 rl = o; 2 ein3z. 2 cos! cos! = o; s in 3.r 0:3,r,rn-nIZ: I=!,ncz;ll a6o cosTr o: 7x n I nh.h.z: ,=!+?!!.k,222277 -.3l^3xn-n2maoo cos 2 ui 2 2 "^,.-Lt x.- 3t 3 .ntL. -finfiznkn2nmBidno6ia)b: :i :- : + .n,k,mF7. s) .E cos5.r + 2sin(-2)cos5.r = 0; cossa(.rE 2srr 2x) = o: 2105 t. J2 2sin2r.. o; ,,"r-=+. 2x=t)f X+nk,k.z: x t t: ftk.h.z. . ,.,n nh Bidnoqidb: | ; ( ir; ;-n-h,7. 862. l) sin,r.sin,3t t, l-'osxrl 'os3}-1. 2222 1 cos ]' + 1 cos 3ir= 2;2 - (cost + cos 3r.) = 2i 2cos 2xcosr=0; coe2r = O, cos r = 0i lz* =! * n,,, cZ, x=n +rn , n. L, 242 _l x=" -ak.hcl: lx " n*.*-2. !+Y.oez. L+nk.kez. 422 2r cosj.r -.osz 2.r + cos'a. t.5, 1+-"2' "osF , I "i"6'= r.l, 1 + cos 2x + 1 + cos 4r + 1 + cos 6r = 3; (cos 2ir + cos 6r) + cos 4r = 0; 2 cos 4,r cos 2x I cos 4x 0i cos 4,r(zcos 2r. , 1) = 0; [:'"41= 0- 2cos2x+1=0i l. n I n nn - I ^ nn l4x= ?tnn,ncz. x Bt 4.nez, lr s.-,n<L. I I r n' I l"o.z' '": u=Lln-!l-rnu.u,t, l, -i,*.a.2. Bidnoeida: ft ft!.a-7, 1L-nP,Ps7. 843 3) cos 2r - cos 8r + cos 6r = 1; 2sin 5r sin 3r - (1 - cos 6r) = 0; 2sin 5r sin 3r - 2sin'z 3r = 0; 2sin 3r.(sin 5, - sin 3r) = 0; 2sin 3a. 2sin.r cos 4iu = 0; 4sin 3, sin r cos 4r = 0! l" sin:.r=0, [3.r n,,,nFz. l' "{.^'z' sinx 0. x=nk,ktZ, x-fik.k.L. cos 4r = 0:cosar=u: fax n t nm.n.z: l"=E-T.^,r BiAntuiAb: :::iitiiiitiii!: AITEEPA Mep3neK A. r. ra iH. AKaaeMi,{Hxn piBeHb *:l 467
  • oe;rr-.atxu 9=nh: n=3h.ro 3 BianosiAb: +,Iezi 4) 1- cosr.=ts,r siD.x: oA3: ,.; "",^czi r-cos.t lll';-"'"', sin.rll-cosr) cosx(l -cosr, sin.r(1-cosx) ^. tc=21th,keZ, ctg.t-1-0, x +f,+ nn, n ez; BianoaiAb:2fik. k e Z. +nm,me7. 4 5) sin t + sin 3:t = 4cos2 xi 2sin 2r cos r 4cos' * = 0; 2cos x(sin 2x 2cos t) = 0; zcos (2sin t cos r - 2 cos t) = 0; 4cos'z r(sin t - 1) - 0; ln. lt=-1fin-naL.cos.r=U, | 2 lstnx-t=o: I nL lx= 2LfiR.neL. Big6ip ropesis:'gas. pzcyso$. BiorLoliOb: ;+ nn, n ez. 6) cos 2r = E(cos, - sin r); (cos' * - sin' r) -'E(co"t z=L+2nh,kez; 7) sin'a + sin'2ju sin'z3r sin'z4r = 0; (sin'? r - sin'z 3jr) + (sin'z 2r - sin' 4r) = 0; (sin, - sin 3r)(sin r + sin 3r) + (sin 2r - sin 4r)(sin 2, + sin 4r) = 0; -zsi'l r cos 2x . 2sin 2x cos x - 2sin r cos 3r . 2sin 3r cos r = 0; 2sin r cos x . zgin 2, cos 2r + 2sin r cos r . 2 sin 3r cos 3, = 0; sin 2r sin 4r + sin 2r sin 6r = 0; sin 2r(sin 4r + sin 6r) = 0; sin 2iu . 2sin 5, cos r - 0;+-.meL,a4 lnl- t" lI= +-,meL. 184 fr-*"-=0, I cosr - sin.r = 0, lco" r * or sin2r = 0, sinsx = 0, cos r = 0; Bidnoafit: t. keZ: L+nl.LeZ. fzx=nn,neZ,i l'x=nk.hez. lx=!+nl,leZ: LZ 2 5 t=!+nI,IeZ. (1- cosxxcos.r - sjn t) ^. lx=2k.kez. t=L+nm.meZ, 4 tir lr + t+ n4 n e L. 8) cos'? r + cost 2r + cos' 3$ + cos' 4x = 2; 1 + cos 2r . 1 + cos 4ru 1+cos6, 1+cos8r ._ -+-+-+- 222 4 + (cos 2t + cos 8t) + (cos 4* + cos 6r) = 4; 2cos 5r cos 3r + 2cos 5r cos r = 0; 2cos 5r(cos 3x + cos r) = 0; 2co3 5r. 2co8 2r cos, = 0; 5r=!+nn.nL7. l,=" "' lcoss:=o. ^-'-*"" "' '-10 l-n,rk- Icos2r 0. 2x " Inh,k-7. x" -tr'!).6a7. lcosr=o: - l ' x=!-nt.teZ: lx=!-ttt.tcz. L2L2 -nnkBidnoBidb: to|--,nezt i,;,k -r. - sin t) = 0; r 3r; 3': + n 6 2x + :+ 2fi 2cos cos : IL6r eZ- 6x z, s9t 2cos ; nl +-nh o;2r 1 2' t-+ cos 9x + 2cos 3x = 0; cos 3r = 0; cos 3js(2cos 6rc + 1) = 0; nn-lnnn 3163 I +2th h ezt l, = +!*!! e "z193 (cosr - sinrxcosr + sinr) - 1E(cos.r - sint) = O; , cosx-sinr=0, lcos-r - sin.rllcosx ' sinx-J2l 0l L ' lcosr'sinx-Vz - 0i cosr sinr=0rctg.t-I -O:ctgx li x=ft -nn.n.Zt cosr+sinx-rE=0r cos x + sin r = .lz : ,Er {cos'+{sin'=r; '12 .12 . n n .... ,. .-rn -l=r, ,-=I -znp.*eztsin4cosx rcos-arnf rt srnl- I -t.) 4 z x=!+nn,nez, , =I * 2nk, k.z. BfinosiAb: !+rm.meZ. 4 468 :}il: AITEEPA Mep3rrKA. r, ra iH. aKaaeMiegnr piaent li{lll:}i.iilil:.i ,- . 1Fcosl2r 1-cos10.r '22 2+cos 12x + cos 10.t = 2; cos 12r + cos 10r = 0; 2cos 11r cos r = 0; , cos11x = o. rtx=|-nn,ncz. -=h-#.,,t. | "."' = o,lcos'rru: ,x n nh,he7: x !.nh.k.Z. .^finn 22 11 iitiili_:ilii-1t1:jii AITEEPA Mep3reKA. r. ra iH. AKaaeMi{Hrt piBeHb lt! 469 I
  • " 1 lrcos2.r I cos4r I+cos6r' I 2) cos' ,r - sin' 2-r + cos 3-r ;: - 2 --Z *- 2 =2i 1 + cos 2r - 1 + cos 4t + 1 + cos 6t = 1; (cos 2t + cos 6r:) + cos 4ir = 0i 2cos4xcos 2, fos4x=Licos4r(2cos2.r+t) ., l;x;;:; =., I " I n nn n,n!.n-z. l4x=-21nn.nLL. lx=B) 4.neL. " e q'. -. .t t- cmzx= j; 1r' rt'2nh.k(L lx -!':t nh.k(z- si3n66166; La!!.16y. a4 3) cos 2t - cos 4]' = sin 6t; 2sin.r sin 3r 2sin 3t(sin t - cos 3t) = 0; sinSr = 0, sin. cos3t = 0; flx=nn.nez, l"', ","{r ,,1 = o, I 2 I ("-i)='' 4 sin2r + cos2x = ."E"i" r; f "inzr+f cos2r=sin.t; sin2rcosl+cos2rsin|= "t'' "t"(r,ni) "t"' = o' . [,",:_lJ n ,.r.[l*ll-"l.'"*ll =0, I 2 I -"-..{ 2 8'"""r 2 st - L"*fr;_l ., l* -n.on.n-2. Ir n+2rn,ncz, 12 8 I 4 l:' s,, - I n 2nk t ^ ,:::"nk-hL7,: tx=-1 .hLz. L2 8 L 4 J .n2nh Bidno6i.Jb: ;+znn,ntzi ; -;'.kez. 5.) cos' x , cosz 2.r. cos2 3r I cos2 4.r: l-cos2x l-cos4r l'cos6r I cos8.r. 2-t 2 T 2 ' 2.os 3' cos r 2cos 7t cos .! = 0: 2cos t(cos 3t - cos 7jr) - 0; 2cos t zsin 5r silr. 2t = O. 47o tii AITEEPA MepsntKa. l-. ra iH. AKaaeMi'{Hl4i piBett ll!.i:iilliiiJtl;i ] sin 5.r = 0, Lsin2r = 0i BiA6ip rcopeniB: BiAnogiAb: It J'= s' 1,,1,,*r.l2 2sir 3, cos 3t = 0; lon l3 l'"*[* ;)-" ,meZ. Bianosiab: !!, h ez., S,nez. 2x=nn,neZ, "o" r, = 1, 2 u, ","u'=r-"13*z*J; "i,' o" = 2sin 2.r; sin 6x sin2x sin2j 0; - lsin 2.r. - 0. 2sjn 2-rcos4n sin 2,r = 0: sin 2"r(2 cos 4x - 1) = 0: lr_"0,_r =0, l'=+.".'. l,=+.^.'.'l qx =,! - zn*. * -2.. l, =, L -!!. o. t.31t22 o.z, xL +4. * ez. 12 2 l,=+.".'. '=!.,.2. lr, "=nu.o.r. l, ;-f;.r,t. l,'i=;'"^,..2, I' i rm.mcz. Bianoliab: T,n ez: !,S,n.z; f,+rm,^ez 2 !6 &F ? = r.r. 2 s65. 11 -l2 l,'x+2 2 r 31 6+5r+10,n. tx+2ltx-21 3-1 3 5 3 5 3(x 2t5(x t 2 x-2 x-2'x-2 x-2-"' lj.+2)(x-2) -"' 8.r.- 4 ^ 8.x+4 - fsx+4=0, ->o: -=u: I tx -2ltx -2t tx-2Xx-21 [(ir-2X-r-2)+0i l2 t Ir n | +-=nn.neL- t2 a I l3v rr r_+_= +nk.ReLi 242 sianouiao, ( -2, -!]u o, t *t. zl o, 2 . A 2 _ 3 .n. ztxr5) 3(l 2-r) <^.-' I 2x .x+5' l-2x x-5-" {1-2xxr r5) --' 2'+10-3+6' 8r,? lS.r-7=0. <0: -<0: 1 (l - 2.r)(-r + 5) (1-zrxr{5) l(l - 2r)(.r - 5) + 0: --i /'-:,-i /- - 57 8 Bidno'idb: l', l].-1 i, --l ::il::i1:$:i:,jt:l AITEEPA Mep3ncK A. r. ra iH. AKaAeMi,{Hrai piBeHb !lt: 1u 2
  • I cnraB ..5 '7 II crnaB vxr ' 7" Paaonr x+Y=28 !'+!,=tE7 7' 866, ,qns po3B'nsyBassa BaAa.{i crina,qeMo ra6,1sitto. S69, 1) sin3 4r + coss 4r = 1 - 0,5 sin 8r; (sin 4.r + cos 4r)(sin'z 4r sin , cos 4r + cos' 4x = 1 - Eirr 4, cos 4t; (sin 4r + cos 4rX1 - sin 4r cos 4r) - (1 - sin 4r cos 4r) = 0; (1 sin 4, cos 4rxsin4r + cos 4a - 1) = 0; (1 - 0,5 sin Srxsin 4r + cos 4r - 1) = 0: I - 0,5sio 8r = 0, I sin Sr = 2, I ueruac xopeaia, fsina-r+cosar - I 0t lsin ar r cos4x.li lsin4r+cos4x=1. -L"i"n',1.*n'=1, .i"a'"""I-.""a'.inr 1, J2J2J2nnJt MaeMo cucreMy: Po3B'fi )ri€Mo Apyre piBsssEs: !-et y=6U7 =zt, s=zr, [x=2a !t, J ze-o *so -,n. 177 t40 -Ua +aa _u. tno;rn =rn, lc = zt' 1tn 2 fifih- lx+v=za. ll'.1,='n' zo 2-! = t a,: 7 BiAnosiAb: 7 Kt I cnnaBy; 21 rr - II cn;rary. 867. sin r + cos r = 1 + sin r cos r; siIIr sinrcost+cos, 1=0; sin r(1 - cos t) - (1 - cos r) = 0' (1 - cos t)(sin , - 1) = 0; T-- d-- , t-cos.r=0, lcos* t, rr=ztrn'nF7' lsinr - 1- o; "in,=r; lx={ .2nk,hcz. L2 Bi,q6ip EopeHiBr arB. ptcysorc. BiAnoai()b: 2nn. n €2 . fr +2nk.heZ. 2 1 868. 1, sin 3x cos 2x = sin 5r; i(sin x ' sin 5r) = sin5x: 2 sin a + sin 5r - 2sin 5x: sin t - sin 5, = 0; -2sin 2t cos 3t = 0; lsin2r = 0, lzx=nn'nez' fcosa' = or lzx = f,+ n*, * ez; BiA6ip &dpeEiB: Ar.rB. prcysoK. ^fifih-Blonoetob:6+n',ReL. I 2t 2coslx t 2o'i cos .r = cos 40"t 2 ; (eoE 20'+ cos(2,. { 20")) cos4o"i cos 20'+ cos(zt + 20') = cos 40'i cos(2t + 20') = cos 40'- cos 20'i cos(24 + 20") = 2 sin 30" sin 10"j cos(2t + 20') = -sin 10'; 2, + 20'= 1(180" arccos(sin 10') + 360"4, n € Z; 2r=+(180' - arccos(sin 10') 20' + 360', n e zi ; = 1l 96' '-srqqeslsin tO't - 10'+ 180' n, n € Z. t2) atanoaiad: t(so" ] *""o",",n r0")l - ro' I t8o' n, n cz. 2) 472 i.l,* ,'IiIIEEPA Mep3reK A. f- ra iH. AKaaeMi.rHran pieexr !ii:iiff.;..;.;!!i ,"t( "'"(*-lJ=#, +,+f,=ttt'!*n .,€z' 4' =( D"f, f,+nn,nez; y = 11y L - !- 1Y. n a7. 16 164 Bianosiab: err" + - #+ f, , n e z. 2) sinBr + Ja cosBr = z*"s'; |"lna,*fcos3'=cosbr; sin3rsin i cos3rcos f, - cossr: coslar-iJ -cos5.!=0: -zx-!. g*-! -2sin 6sin 6=o: 22 3) cos 2.r + sin2: = rD(cos'2r - sin'2*); cos2r + sin 2r = Jt(cost 2.r + sint 2rxcos' 2r - sin'? 2r); (cos 2r + sin 2r) E(coszr - sin 2r)(cos 2t + sit2al =O; , tcos 2-r r sin 2,r - o. (cos2-r + sin 2rl(l - V2(cos2x - sin 2.r), . 0i r-rc2.r=o, II v2(coszt sin2t)=o; l+=-.r,-"*r,. lJz a) 1+ ts 2r=0; ts2x=1; 2z=-!+nn,nez; x=-[+l,nez; 6) cos 2ir sin 2r- | ; *"o" z* - *"tn z* = 1;'J2J2J22 coslcos2x-sinlsinz'=1, *"lz'.') r' 2, , ! = - * z,*. * . z, 4 4 2 4) 2 4 3 zx = t!- l+ znn, x ez; z = tfi -[+ n*, n ez. ^ fiItn _ 1l 1r Bi0no6i0b: ;t ,neZt !:-:+nk,kcZ. ilili:i:tjlli-itiAnrEEPA Mep3rtKA. r. ra iH. AxaaeMiqHxi piBeHb::it 473
  • '1 azo. 1') 2cos4:21= x, + 4r + 6: 2"o,t !!1 = ," ,, 4r,, 4,,2. 2"o"t-!3a = 6 + z)" , r, "o"t1?' = !r'+ 2)2 + r; piBBrEEs Ma€ RopeHi, "*uo |{,+zl" =o; t = z. BiAnosiob: -2. 2l grn!1 = " - 4" * 5; "i.n14- = "" - 4r * n+ 1; sin 11 = (r - 2), + 1, piBEsEss Mae KopeEi, rKryo (t - 2rz = O; t = 2. BiAnoqidb:2. 7. Po3B'r3yBaHHr Haf npocriulrnx rpl,iroHoMerpr{Etax HepiBrlocyefi 821. r) su.t < ]; -U+2nn<r<!+2nn,nez. BiAnMiA6: (-!*zn,t!,zn^.o.2. trtj) t; 2 -!+znn<x<!+znn-nez-44 BiAnMiA6: (-i,2,,,! * z^1.,.t. Z) si.rr > -f ; -!+2nn<x.s!+znn,nez. BiAnosiAb: |-!*rnn ! n ro,], n.t. t; 4) cos r 5 J9; n l7n -+zfinSx<-+2fin,neZ, 5) te, < -l; nfi -- + nn < t < - - + ,tn, n e Z. BL0noqidb: (x z l -+nnt- +nn),nez. ?) ctgr < f3; n -Bianosiab: lt+ thi n* n,)., n.z. 9) sinr < ;; -n - arcsinl + 2nn <.r < arcsinl + 2nn, ne Z. or tsx>f ; [+nn<x<!+nn,rez. Bia,o6ia,,li t>-1t 3r 4 sianoaioa: (trn: ! + nn), n ez. 10) tgr > 3; -|+ nn < t <|+ no, o ez. +ftn;-+nn).neZ. nn, n eZ. 8) ctg i BiAnosidb: f;, r^,t!t n r^,],,.t. BiAno6iAb: (-,, - *""in I * znr; *""i" 1* zn"), ne Z. ;i:llilillllilii Ai|-EEPA Mep3.nr( A. r. ra iH. A(aaeMi.rHri piBeFb li:i: 47S Bi0nosiAb: (" z l-t+lutt+nn),nez. + in < x < T + Itn, n aZ. a7a l:i!i urespl Mep3reK A. r. ra iH. AKaaeMi{r.nr pieenu Lll!ill{:!ili.:;!
  • ezz. t) sinx <!; -! + znn < z <f,+ znn, n ez. BiAnosi1b: lsn ' - l| -- + 2ftn. +21tnl.nez. 144) rr "n. r < 1, '2 L+zn<t.!!+zn".nez. BiAnogiAb: lL*z^.,4*z^,].,.2. L3 3 I 5) tgr>-1; -+rn<t<+nr.nez.42 2r sin r > -1:2 -! * 2nn 3 ,3!A a 2n1. ,y 67. 66 BiAno6i0b: I ! , z,^,!! * zon). n .2. 16 6 ) 1; nr "."" f r -L+2nn<tsL+2nn.neZ,66 BiAnoqiAb: - l-:*2"";:*2"")'".2 O; tg .t < -",6; -|+rn<'<-!+n","e2. BiAnoaiAb: ln n ) I t+ ltnt - 3+nn),neL. t; '3 nn<t<-+nn, ne Z. aianoeiat: (nn;!+ nn), n ez. s) cosr > f; -"r""o" | + 2n, . ". ur *",f; * zn,, (- **." | * ,no, u."" o"f,, zn ), o . 873. 1) sin 2.r > f ; !+2nn<2x<!+znn,nez; ! +nn < x <1+ nn, n ez. 8)ctgx<1; f,+nn<x<n+nn,nez. Bianosi1b: (arcclg 2 + nn, fi + nn), ne z. a €(-;) .v6' ,ei, Ji' rtn--+1tn<-<-+Itn,naz, !+4nn<x<2n+4nn,nez, BiAtuosiAb: !+n",L+"n.1.".2. ,6 3 ) l--+nn: +ttnl-n€L. L4 2 ) BiAnoeiAb: Bia oBi,b: | -1! + 4nn; 2n + +nn l. n e z. ir) f, ra iH. AKaIeMi.{Hr,rfi pieenu llJ sianoaia': I! + nn n+n^)..e 14 ) 10) cLgr <2i arcctg2+nn<t<n+nn,ne 476 iii: AnTEEPA Mep3nr( A. r. ra iH. aKaAeMi'rHrr pieexu it!:illtli:iJ:::!, :ilil:igllll*ti AnTEEPA Mep3"K a.
  • 3) cts 5' > 1; n+nn<5r<!+nn.neZi4 finn+ .n€L. 5205 Bidnosdb: ( ! | L + !!). n E z. 5 20 5) ll 4) cos( 3x) > ;: cos3r > t: 11 -arccos; r 2,'In 3x. arc.os I t2^n,n-Zi tt2nnIl2nnI <Ja<-STCCOS +- ,na/. 333333 ( I 1, 2nn 1 I z,Tnl Bidrodidb. l-5a'ccos3r- r 3ar.rosA I 3In a74. 1r sin{ < 1r -U*2,,.!.!42nn-,E7.636 7fi --+tifin<r<-+tftn.ne4.22 ,, *'l {) '"6, cts{. "6; 5]Ir- -+nn<-<T+nn.neLi !!+znn<x<2x+2nn.nez. 3 Bionotiab: (+ + 2nnt 2n + znn), n e z. 3) te 2,r < -;: L+n,<z'<-+nn.nez: 26 nfin+-<I<--+.neL. !nftn n nnl Bidno6i0b: -i+ tt - i+ t ). n e L. 1 4 11 arccos i + 2nn - ar < 2,T arccos- 'znn,n-7i44 l lrn nl 1nn 4422442 ,l I nn r I 1 nn Bidnosidb: iirreos- - 2i 2-iarccos-+nl.ncL. /- 875. 1) tq x-llsJS;t r/ _!*nn., r. +nn.,.2, -1+ 1+ jrn<r<I+ L+n,.net, n2n - +nn<r<-+nn-ne7- 63 T- llLalnoBLtlh: - +ftn- +frn ne), L6 3 l 2nn2nn T+ 6-2nn2t< Z t-+2nn.n€Zi !+2nn<2t<!+2na.ae7' 26 fi5fi --+1ln<x< +fin,neL, - (n 5Jr )it@no8db: l-i+ nni-+ n ), tr e L. ' "*(;-r'#, "-(,-l,),*, "ic(,-i).-;, v 2nr +ltn<x-:<fi+nn.n€7i 2fitift i+i+^n<x<n+ +nn,neZl llfi 5'I _ +nn<x<-+1tn.n€L. (tln hn Bidnogidb: l + nni - + fin ).4 eZ. 4) 2srnlI-3xl< J:: sihl ax- Il- '6. "i"l s,-Il' - /3. ti ,r 6) 2 61 2 :: + 2ttn < 3, _ t: < ::: + znn n e 7 : 363 ! 1! n 211n. 3r. !! + ! + 2nn. n e 7.: 3636 -L + znn <sx <1! + zn,. n e 2., 62 n 2fin n 2nn - + t)aa_+-.nF/.-1832s I n 2nn n zrn)llidnoaidb: - + : +- ne7 118 s 2 3l sr "n"l{*rl<-f,2 4J 2 !.z, <|*|<!+2nn,n.z' t+zfin<-<n+znn,ne7: T+ 4nn<r<2n+ 4nn, ne Z. BiAnMiAb: ln + 4nn; 2n + 4nnl, n e Z. 47g li:l ATTEEPA Mep3rer A. r. ra iH. aKaaeMi.iHur piaexs :i:iiiJlil{l:ii;i i :iiiii:iiiltii:ti AITEEPA Mep3rqK A. r. ra iH. A(aAeMi,{Hrr piBeHb !:!l: 479
  • 6) sjntr _ zrr . _@. o ^ -"'' -T' -"'n,r" -tt. -f ; sj,r2.r _r)> i + 2nn < 2x - t. ! * roo.,.,. n" I' 'r' "- "* ,T ' t '2on. n u z, "-r..*"..t-j,+na.nez.Bidnoaidb: (! + : + ^r, 3 * f * _- ) , , ,,,,I,nez. e7o. rr "t"f,*Il- E -| 6/:vt'i nn<x4lI<ft tr A'6+n"'o.r'-E+^h<rSnn,nez s, -"1*_rl,l. 6)-2, -Ir2*r*_[r{*r*.,.r, -i+u +2nn s,rsr* !+2nn,nez, -u+2xn<r<[+znn,nez. ffi 3nn ;--+2nn<a,n n i- ' 2'i-;+2nn.neZi ii*2"".|.ff*znn,ouz,r 77n sinl r-:11-, s)- 3) -2<tgr<8. n aZ. 4) -1< cte, s JB. c 2 Bi0noaiOb: {-.arctg2+,rri srctg g +fin),n€2. Bidnostab: ",u*",u", f_ ; * rn,, | * zo,l. o u z. er ":n/e.*I)- 6 .2n n tt =-V: -f - zxn t o, - ! , - I - "o,, n-]-5 .2nnsr*s -[. lr, rnn. n.r, -;=+2nn<z-- Bn ,,j -.^ =_G+2nn,neZi -ff*f s*s-?l-^, _ _ tE z ,,, . z. Bidnosiob: l' !7! , nn 2n __- - i 60 i'-l;-V1.,.2. 877. lt r* = "o",. lz -^'t ^ r , _, s sinr < !rnon.,.$*on,,o,i. a'a^"tu"' (! r nnn: tJr r axnl, n e z. ar z"i"/f -*j.r, _"in/* _tl. t. - :-,^*.. #.,:, r^,.,!,,' ^i. t' ^^,..,. ! . !.,,,. ^.,, i*rnn.,.#*rnr.n.r. "'u'*tu,' ( [ - r*, ! + zt,), o e z. .,*(;.;1.f, [-,8*2",'-]*z"n)u t,/ I * ,--. sz I 3 -"'"8+z^n].nez. [-,6 * zo", un":" ] r znnJu tl o -"""un!*zn, 3I* 2o,,], ii:ii:iiiiii:;iii AnrEEpr rrr.p"r"^;. ""'"4 Ld " nn; ::: - M I' n . z. rh !,, r4e,nM. r l --"'^^' r' ra iH. Arag.ri""r,i pi".r" ii,ji,, +8t
  • ./3 r 878. 1) -; < cos x < Bionoaida: | 5n, znn, 2! r'1. l?-*"'T zr J<"r*'<j. 3) -4<ctgt<1,5. ll -@. tg'. r. BiAnosiAb: (arcctgl,s + fin; n arcctg 4 + "tn.r, ":r:=4(€-t)=Va-Ja Ja(Va-rl d*"" * sit^""- "Eii("t; r a"6) '' ,t^4iii . sG r'r*,,t,t' - {n ' 311;i + a{nm + sJi (G t aa,E)' a+8 ({; *z(e["" -zli*n) 8so. 1) E !E:!)' .o' 1lfSf = o, BiAnMiAb: L3; -2)u (-2i 1). t'-st+4 x'z 5x+4 2l ->0: -=U: 'r'-6r+8 -r' 6r+8 f.r=4a6oir=1; lxr4a6ox+2. [t:-rrrx+rt'= 0: [x = 1a6o r = -3r lrr+zr'?*o; l'. z. 2 -2 -1 * zn,), ,.2. -4 BiAno6iAb: nn), n eZ. =16+1; XE; tn n ) l- 6+nnt +Itn),neL. finnnnn 6262 (ta-rX"6.r) <Ja -r ;,'-:/'-:/-+ It'z - sx + + = o: lrx- nXr -rt = or lx'-er+s+o; l{x ax-r-2)+oi BiAnoqiAb: C*: 1l u (2i 4) u (4; +-). ", (r + l)t.r 3f , ^. (x + 1)lx - 31'? 0; t+4 x+4 fr'-tx'-at'-0,' la6o-r=3. l:c+4+o; lr* +. BionosiAb: ( 4; -11; {3}. Aal. noAis A rossa AinLEr.rEa rrrcna 32. Airbllr.:Kr.r 32r 1, 2, 4, 8, 16, 21. ,l.l'63 Pl Al = -''n32 16 Bidnoeidt: 3 16 .l; gg2. t) lcosr 'Y; -'l ' nn- x<'! + nn, n -2.'244 zl Ei"zr.*; rr ,t --+[z<x< +nn.neL: 66 n2n -+nn<x< ^ +nn.neL. Bidno'idb: | ; "J, ;- T).,.r :litlit{i!:llil A'||EEPA Mep3nrKA. r. ra iH. AKaAeMieH}rr piBeHb ::* +)/-:Y-rf+ , t/.=/,'i/-+ Bianoeiao: I i. "",i. ""1, ".2. 482 itl: AnTEEPA Mep3reK A. r. ra iH. aKaAeMieHltt piBeHb lliilliltl:liiii 443
  • 4) lcts irl > 5. '.i"'(,-i), "a, "u(, -;]'*, nn < , -! <! + nn, n ez: ea3. r) sin'f +cos'f '|; "n'f .2"r"'fco"'f +cos'l-zsio';"""';'rl t ^' ".rr 1r2x I - | ,2x f lsin';" cos'fJ -2"'r"T,2: r- 2srn T>2t -' '1"T,-t, r-"os1'<2: "o"rr.r,2223U ar 3rr 3nrt cos a> l: ;?n -2nn.nezi xa 4--.ncz Bianoliab: r e n,"vi* !+!,nez- a ",(; - "). """(r - "; ..,e, "'"[i - (t. l). "*(; -,)',r, *"(; - I - """(; - I > Jr; 2"o"fi "o"' >.,6, r. f "o", = n6, cos t>!1 x=2nn, n€ 2. BiAnosiAb:%n,neZ. 3) sin , > cos ,; sint-cosx>0; ,- "i" ' - sin{ tr-.rl>or z"tnl *-I]cosn =0,- "^ "'l2 ""1- -' --"-l 4) 4 ,","1 ' 4] @=0, "i,'l' 4l zo, . 4) 2 4' 2nn< r -L <n + 2nn. n eZ: 4 L+zn <x<4+2nn.nez. 44 BidnBiab: i+zttnt - + zltn I n e L. +t ]lajYr J5; oA3: sin'-cos,*o; te'+1; "in"-"i.1 ft 'l z"t^**"l." "l" -"'2 '-) t; 4 4). t;. ln I - I ,rl ,I sin .r - sin | 2 - .r J zsrn ['x - ;.]cos 4 rrttfi, -+Tn< x < 6+i+fin,nez: fi5,I+rrn<x<-+1ln.neL. ^ lft 5n )Blono6tdb: + ^ni - + ftn ), n e L. sea. ry rcosrcosl x+l''G, ,'"o, z, '[1 -"il' fe, 6, t "o.l z'* 1l- €'4, *"1 z**11'0, 61226,/ +2nn<2t+ <-+zftn-nel: 262 2n 1t +znn<Zr<-+Zltn.neLi 1l It --+fin<x< 6+trn,neL, Bianosidb: l -L + nn. ! + no l - n e z. 2) 3 + 2sin 3r sin.r > 3cos 2r;3(1 - cos 2r) + 2sin 3, sin .' > 0; csin'z, + 2sin 3, sin r > 0; 2sin r(3sin t + sin 3t) > 0; 2sin r(2sin r + 2sin 2r cos r) > 0; 2sin r(zsin .r + 4sin, cos'?r) > 0; | - - + frn: - + fin l. n e L. 3 3 t BiAnosio': (nn: atcctg 5 + trt) u u (n -- arcctg 5 +MI|fi+nr"), tueZ. .4sin'z r(1 + zcos'z r) > 0; 1+2cos2r>0npl,lr€-Ri sin': , * 0i sin Jr + 0; x+|tn, ne Z. BiAnoaiAb:x+ML,neZ. 885, 1)2cos'z,+3cosr- 2 <0. SaMiEs: cos, = t,, € [-1; 11. It_- t+-+Ilk,ReL. 2t,+3t-2<0i 2t'+3t 2-0i D=25: -3r5 1 t,,= a i tt=tl t = 2: -l<t<!: -r<"o"r.1.2 /- Bfinoeidu lL + znnl !: + 2nnl|, n ez. z1 ts" +(2 - "ls)rs x 2h <0. al lte '1. Ja. -----+->.2-/z'? . SaMiira: tg r = t. -2 -./6 t' + (2 - s)t - zJz = o; t" * (z - Ja)t - zJa = o; i::::;:::::::ii:i:::::i:: AIrEEPA Mep3ntl( A. f. ra iH. AKaAeMi,rHri piBeHb i:ii:484 ii:: anrEEPA Mep3neK A. r. ra iH. AKaaeMi'{Hrt piBeflb li{llliiiit:alti
  • r .o = (z - J5)' * e'6 = a r.,E + (.6)' + s"E = = + * +.,6 *(.,8)' = (z n Ji' ; . z*'6t(z*.F),,"= 2 , t,= 2; t,=.ft; -2 . I . 1E; - Z . tg r < Jt . !n) Bidnoqidb: l-arctc2 ' n ;-n ),nc7- | ", 2,,, 3n . -zn,), ( " - r"", lt' r,',,.] - f s., znn: 2n t 2nn). n c z.Ls 5 5 / h ) 8, BnpaBll Are noBTopeHHr Kypcy anre6pra ra noqar(iB aHari3y lO Kracy 1. MHoxnHx. OnepaqiiHaA MHoxnHaMn 886..4 ^ a a. C - MHoxxHa HBaapariB. AA7.A., B=C,C MHolrrHa kBanpariB. 888-I)AwA=At 2rA^A=4. 2AJB=4.0; 489. 1).4^B=B; A9O. 1) 35 - 10 = 25 wsip ozeqaprB i Oi3r-rlcy, i MareMarnriy; 2) 25 20 = 5 ]J"{]liB saiiMamrbcs nsEre abistrRoro; 3) 11 5 -G y.rriD 3aiiuanrrcs i nareuarqriolo, i ibi3lrRolo. Brdnosidb: 6 y.!1i'. 2, OyHKrr;r_, piBHrHHr, HepiBHocri Agl.l) /(xr=JJ-5: ,ln:r 5>0ijrt5:xc 15:,€l: zl fto- -]:; D(fr:4 - x> ot r,4; r e (-*;4r; .J4 t 3r /txt ,.s ,; Dtlttx'z-5aoi x*.Js: *.{ *, Jr)r{ Js,Js),-{Jsr '-}, 4t ft*=f;AtDtntx€Ri 5) i (*) 7j+]3r D(t)t x'-7x+o.x(x - 7)-{):.r-ua6or* ?i r'-7t .r€ ( 6; 0)u(0 7)u(7;+-); 6) /(irJ r,; DtD; I,rl -3-o;lxl*3; x--3a6o s: uiJ ju€ ( -; 3)u( 3; 3)u(3; +-); Zl 1111= --L. Dtf). x e Rt ln +l) 81 /1r1= ll , D(f): l-Yl .r' / 0:,r > oi ,rr ,r , 0: ,r(,r - l) ' 0: lx+r' r + O e6o x + -1, BpaxoByroql,I., > 0, r I 0. r < Ot x' - x + Oi x(x - 1) + oi t + oi t + 1; Bpar{oByroqr .! < 0,,c I 0; r € (--; 0) u (0; +-); fr , 5:0: fr u 5: 9) /(r)= J.r - 5 - V3 - n; ,(n: 1 I x.t5; 3l; lJ-r.]U: l.raU: . r+r lr-l>o: l::r: 10) /(r, Jr It " ,--i D(l)t I { .rc tl: l0)u(10; -):x-10 Lr/1ol ljr/l0r 3),""",(,+;)'","(;-r, r; z".r(,*i)-as.[j-[t'',,)).'''., /_ r""Jl '+11 :cosi r+al+1>0. 6l 6.r /.saMiHa: coslr -;J /. I . [-1: I l. 2t' - 3t t 2t, - 3t + 1=o; D =1; t.,=f; r,=r; Il nrl i^= ; -l:i.;r licosl,r r6J<t: L n 2nn 5 t 1L.5! 12nn, n .7, 363 [+znn.".!*zn,,n.z. Bidnosrdb: II t znn:T ' 2,,), n.z. 6 2 ) 4) tg x > 2ctg t; tgt - 2ctg .r > 0j l^1t+ +ftn-neLi oA3: I 2 lx+k,keZ. tg" x 2 > o. BaMiEa: tgr= 1. tgt t'-2.o. r-2=0. {r, -.Eacoi. --Jz: t t [t+0i -nE <t.o a6o r > J2; ,,E<tst<o a6o tg'>'12. Bidnoaida: I-arcteJ2 ',.nrnn)t u'.ug.,6' ,.r, |-nnl.,.z2t 5) sin 2, - sin 3.,. > 0; -z"inf *"f ' o; 2"i^;."s5+ < ot 2st";*"? = 0; l .i' l = 0, x^ nk- k cZ: l, ^o. u -t, lx = 2nh. k'zl | 2 l2 lz i ft 2nn J*"tj =0, l'i i-",.^.r, lsx=n t znn'ncz: l' s+ b 'ncL 486 Iti: AJII.EEPA MepsreKa. l-. ra iH. A(aaeMieHnr piBenr ili:llfJi:i:j:.tji iia:j:iaii{iilti: AITEEPA Mep3rqx a, r, ra iH. aKaaeMi,{Hnr piaenr !il! a8z
  • 11) 14) lr 2 2o. lx>21 Jtxt Jx-z, J2-xt Dtht z_r,o,, ,. zi,r, t, q>o: lx>9: r€ u.ftx = Jx -9 + --::; D( l - 1E-; -" 18-x'0t [n-8: v _7 lr_2_0: I.r: ,, ,. t_2:21, t2i t_.Ji ftxt=J! 2-i o;othtlx 4,oi lxF_2ix t2i ,,-T 5x -4 Jr+3 .r'-6x+ I 893. 1) /{).) = -; .x+2 D(ftx+2+0:)e + 2i -. tx - 2(x + 2 flxl=-=x-zi a+2 f(tl = x 2; 2) fr.rr=r -6r+9: ,(f):3-r*0;x+3i - {x -3)'? (3 -.r)'z ^ f(r) = 3 q I fx-620t fr>o: Drfl: ]x+3>o: ]*' e: Lx'?- 8r+7 + 0i I'r + 7 a6o -r * l: r € [6; 7] u (7; +-); rrt ff,l = J-"t- e, + 9; ,(f): x' - 8ri + I > O; r,+8.r-9<0;x'+8r-9=0; , = 100; It= 9i r,= 1;, e [-9; 1l; l116) f(x)=-+ '- ; ' Jx' +6x_7 x' zx Drn, I"*6* 7'o' *.*6'-?' o, '' lr, _2x+01 t,+6r-7=9tJ= 7t xz=1) {t + 2, + Oi r + Ot t + 2; xe ( -i -7) u (1; 2) ---i,,-- -,/-- 9tjc - =/-/'-,-70 12 l7t ttxt=Jx-6+ _=- l 'l x' - 4x -12 lr-6>0r fx:6; D(n',' a* - rz, o; 1*' a,-tz,o. t, 4x-12>o;t! 4x-12=oi= 2tx, 6 r-5 18r l{x) = Ji;;- Br' + xL e i hs' a'' t o, l3r(5 -.r) > o; o'n' 1"" n , o, 1" -r. x F (0; 3, u (3i 5). 892. 1) l(,)=#+L Z(D: t1; +-); y=G vropv sa I o,qxH4qro; 2 to4 = 'G 2; E(ft | 2; +*li v = J7 vsns Ha 2 osr'rql,lqi; 3) c@J=3- tt E(er; ( -;31; y= x'yropy lra 3 oal.rE{qi; 4) f(tt = x' + 2i E(nt I2t +-); v = ,' vropv tla 2 oauErqi; 5) e(t) = 5 + ItL; E(q): [5; +-);v= r vropv sa 5 oarHlrqb; 6 h('-JVa-5; E(t): t-s; +-); 7 t(' = 'l-x't E(ft alt s, /rn) fira .li - xt ortt: 1; ; . ;, t; . ;, x 3i E(n' toti s) f(t)=Jl-"'; t(D: to;11; 10) flirt =:r E{n: (0i +-). 488 r::.j:: ATrEEPA Mep3ncK A. f. ra iH. AKaaeMi'{Hr4i piBeHb ::i:::::::::i:::::::::::i: 4.x - 20 3) I(xl=-'x' 5.f, D(f): x' - 5x + Oi x(x 5, + 0l r+0tx+5; - 4rx 51 4 4 xt= .:=-i Jx)= i -r(.r - b) x 4 tG = 5=: Dff : x.+ !1; f(' = 1. |ga. f(4=Jx+7; fl")=o; G+z=o; r+7=o;r=-7i - r"+4x 5 -. Z) /l,rl = -: /{x, = ui t? +4x_5 lx,,ar S 0: x=_Sa6on l; _ =(l: I x b: ,r-l [x-l*0: lr/l: e1 nx1=uQ at fl')=0; rt' 6=O; x' a=o; r"=a; x=xr6 q f @ = (x - sJi-r t(')=o; (n-s)G-=o; x-3=0: lr=3:I r=3a6oJ.=4. LJ'-a=0: r=ar iili::ttii:;lil{i AITEEPA Mep3riKA. r. ra iH. AKaAeMi.rHrn piaexs lf:i 0 2 v 0 0 2 U I 1 2 8 U 4 2 1 0.5
  • [-9,o*,qo*<r; I.r 895. 1l frr)= j-x 2.sKDro 4<x<2i 8- L- .'nqojr>z. u1 1'1 = -9, "l,,"Poo,,u, 499, 1) l(x) = 0 (ro.*ca reperrHy s Or), 2 I(o' pesi; 2) flr) = ll Mae xoqa 6 oanH Kopisb, nKqo a e l2i +*: 3) flr) = a Mae aBa KopeHi rpr a € (-2; 0); 4) /(jr) = a Ma€ piBHo oarH l{opiEb rrpz d € (1; +-). i I I I sifl iftfl rry 9oo. 1) l(r) = 7ic6; D(f)i t i ( -; +*); /( r) = 7( r)t = ?,6, rapEa; 2) fG) = 3r5 - 2r1. D(|Ji r € ( *; +*); fl-r) = 3(-'f - 2(-t)? = 3r5 + 2'1 = (3r3 2,?), I{enapl]a; 6) l(r) = x-2,rpsMa; 1 1 U 1 3 e) l(r) = -9, .inep6ora; 2 4 8 16 4 -2 -1 -0,5 l(r) spocrae IIa (-*; 411€ sal2; +*); l(r.) crana€ Ha [ 4; 2]' fs.rxuor<-2: 2r ftr) = lx' - 2x - 3, n.Rrrjo -2 < x < 4i lz' a, u*qo ' > +. ^) f(,, = 5, npsMa lapanenblra o'; 6) ^x)= !) 2x- 3. napa6o,ra. {Birkr'r, eKor FarpaBned Bropyi r'" =: = t u"=1-2 3=-4,(1;-4lt B) l(r) = 2t 3, npnMa; 4 5 a 5 7 f(r) Bpocrae tla [1; +-); l(r) cnanae Ea [ 2; 1]. ee6. r) l(n)=1t-+tE-x; o(ft: 2) f(x = J-r' + ';D(fi a'z+t>0it'- t<O;x(t 2)<Ot r € [0; 1]. 8s7. lt f tx) = tG s + Ji1: ft: 'at: I Lgxrrox<2: 2t fl)ct = I U. EKUro 'r > 2i 3,) ftx) x:. nxuo D{/r: (lt.E). ro E(n: {l: 2r' 49O il:::AIrEEPA MepsneKA. f. ra iH. AKaaeMi'{Hraf piBeHb ::::i:::::::i::::::::*::: z) f(i=+-; DU)t',-5+ot x+):.15; ". (*; - "6). (-"6, l5), (,6; * -); s) f(x)=ls-"; D(f)t I r' > Ot 11 = -3; r, = 3; r € [-3; 3]! f1,1= nG - 1-ar = urg ;, ".o"". 5 f(r)= x' - x +Li D(f): r€ R, f( ')=( ')' ( :. + t= r' 3ararbEoro Bnrnsayj l 6) /(.r) = ,:: Dlf" 11 ! ' ot !l! I) / oi .r € (--; -1) u ( 1; 0) u (0; 1) u (1; +-); 3r r-r+liibvHKqin (*i 2t w (-2; 0) u (0; 2) u (2; +*); tr" 2x't | - 2r" ^ . ovHxtlls G' ax) r'-4x 111/{-r)=- i HPnapHa: ' r.Yf (x) x'+x 7l f(r = (x - 2ll (t + 2)" D(n: )e e ( -t +-)i f( :t) = (-:. - 2)l - (-r + 2)a = ( Q+2)ra ( (t 2)r1 =(x+2)4-(r-2f = - -((x - 214 - (t + 2)i), senapHa; 8) /(r)'-'l . DD:Zx+6-0;n=-3:.r=( -: 3)-( 3r -): ,(n He c4MerprlrHa BiaEocEo ro.rrcr O, i(r) ibyE&rrir saran6Eoro BlIrrEAy; 9) fl,) = r3lxl; r(D: x e (--; +*); l(-r) = -(-,.f-t = 13,r, I]erapHa; l0r frx)=+;t' 4t l I I j I D(fl. ic& 4x+O; t+Oi r t!2i r e ". I x)"+21 xf x3+2x'z Gr" - 4( r) x' + 4x lr s>o; Jx:5: Lb-.r>o: lrssi 9O1. 1) y = 3t + 9; B'rpu*""to t ""p"" y, t = !:!. fiosEaqliMo B oaepi*ranifi QopMy,li apryMeEr.repe3 r, a OyEXrIno - qepes y. MaeMo r-g , I ^Qysnqrrc r= 3 aoo v=t,r r. n , 6=!;,=!*e. ro3'a.rr.rMo apryMeHrt, , , _6, Brpa}HacMo r qepe3 9: g s trcpe3 .r. a OyHxniro qepe3 g. MacMo OyqK(iro y 4 - e. Al a = 1,E:n (ArB. nosclevt.r ao saBAarHs 1); u5 r 2.rt 2x r.u..,=1_1,, ,=1_1",2 2" ' 2 2 iliilili{iitil A'TEEPA Mep3rrK A. r. ra iH. AKaaeMi,{Hri piBeHb ii;:i 491 4 8 -16 g 2 1 0,5 1 0 2 3 v o -3 0
  • 4) a=2-nli-4; nE-1,=z y; '-4=4 4g+a';t:=g'z 4v+8ta=x' 4r+8' 5ts x'ixc [1r--)r x= Ji, v'"G. 6)a=xu;ze(-*;-21; "=-Pli; u= G- 9O2. 1) Ocld,'lbftr piBEsItEs y = l(r) Mee €AllHuii xopilrb Bi{nocso 3MiIIEoi t, ro rBep- anieEEs npaB[nEr{e. 2) TaIl, oclcitERv piBlInHEfl y = l(t) Mae €Alsri liopiEr, BiAHocso 3MiHHoi r' 3) Ei, ocnir6rcr.I piBHnnna y = l(.r) riroxe uatlt ABa KopeEi BiAHocEo sMiEEoi a. 4) Hi, y = g1g 1- t.rapHa, y = arccig t - OvHrcqis sara"lrHoro Blrrnaav. 5) Tax, ocRin6&{ y = '3, D(g, , € RtE(itae n; c={;; D@ 'e Ri EG): e c Ri Dlgl ElCl, Elgl = DIV' 6) Hi, ocni,rrxa y =;rat D( tt.Ii;t(y):[0i +6 c=!t, D(g)t )ee R. E(g); t0; +-); D(y) + t(s). 9O3. 1) (2t 3X3r + 2Xr 9) < 0. nocniAoBHicrb po3B's3vBaIIIIs: 1. 3Eafrrn o,43. 2. nepeHecrr Bci q,reHtr HepiBuocri BniBo. 3. fiprpiBEsrn niBy.racrxHy,4o Eyrs i sHaiira ftopesi orpnMaEoro piBssHEs. 4, Iloana.rarr.r orp&Maxi qzcna n O,q3 IIa qncnoBiii 4psMii. 5, BMrsaqurrj BFak Oyltftrii Ea xoxHoMy npoMir{Ky. 6. Senrcarr Bi,qroBiAb. 51 !:I2 6, -1:!r6, IJ36'' r-2 r-2 x-2 OAg'.x-2+O;z+2i I:!=0, r-5=o:r=5.x-2 BiAnNiAb: (2i 51. 6) 1]]4 s o; '1 * t'-u . o, ': "'! , o, 2-5x 5x 2 5x-2 On3| 5t 2+OixxO,4i 4i l'6 o, 2x r r.6 - o: -r = ,0.8. 5x2 Bi0tuosiA6: ( -; 0,81 u (0,4; +-). ?) (r-ll)(n--4) lo; o,u3:.r - 10 = o; r =' r-1O t-.1-11)411) = e, (, rll)(J r4) o; r-10 fr+11=0: Ir= rri lr+n=or lr=-1. BiAno'iAb: | 11; 4l u (10; +-). (.r+6X"r-8) o-Il3: t.r + 6t{r 8) + 0, ' * -"' i*a r -&l- = 6; x - 2,i =o; x= 2,s. (r+6)(r-8) BiAnoqiAb: (-; -6) u [2,5; 8). so+. rr tl -!*'1'o; o.zl3:x'?r6.r rE,u;'x'+6.Y+8 x'z-5x+4 - " -"" -" !=0; x, _ 5x + 4 = O; x = 4; x = (.t 4Xr - 1) ^ (t+4(t+2 BiqnosiAb: (*i -4) u (-2; 1) u (4; +-). 2l^ i '^.O: OJIS: .rr - I - 0; .r * -13. xr 3x' 2x 0: xq 3x, .t 2x = Oi xtx, - 3x + 2) = 0: xt= O: x2= Ii x,= 2. x'9 '!'-])'-!.0. W(,-3)(r+3) ,B o I z iJ Bianoeiob: ( -; -3 u (0; 1) !-) (2; 3). s, , * 1> 1, o-[3: ,r + o. !2 ''1 I'o' 2x'- bx-2 >o 2x,-bx-z=tJ;32 2x . zt,-zt( r !) D=9:r 2: x^ r: ' z':0. "22x - - .TY=Y* :012^ aianoeiat: (o;!)wP; + *t. z ttillti:jliiliii AITEEPA MepsrrKA. r, ra iH, AKaAeMiqHrfi piBeHh tltj 493 -0,8 o,4 10; --a,ti'-T.. -11 -4 lo r OA3: r € fi. Qx-a(t+2)('-s)=0; i'=r.r=t1, lzx-a=o: | 2 la'*z=0, l*=-f, Lr_e=or lr=e. niaoouiao, I :, - ?f .i ; I 3t tz 2)(6+r)(r+2X4-x)>0; O,43:,'eR.' [,r+o=o; {-r+6X.r+ 2)(x 4l=0: lx+2=0: lx-4=0; BtAno6i0b: (--t 6) u (-2; 4). lx + 4: lx + -2. 1;,1. I (' + 6)(, + 2Xr 4> z--61 0i(r+6X'12)(t-4)<Ol ffi 4,8 15 3) (' + 4,8X1 - x)(5 - x)<0iQt + 4,8)(, - lxr 5)< 0; O,4B: ' e -8. (t + 4,8Xr - 1)(t 5) = 0; lr++.8=0r lr=-4,8;tt lx-1=0; lr=1: Ljr 5=0; Lt=5. BionosiAb: F*t 4,81 u [1; 5], at j-1220, o.[3: x 8.4-0ix/8,4. t 4.4 -_" n- = Ol r 7,2=0ix=1,2. Bilnosi.Ab: ( -; 1,21 u (8;4; +-). 492 r:i!.: AITEEPA Mep3neK A. r. ra iH. AKaaeMi'rHrr piBeHb :i1ti::rj:r::ii;:{
  • $ 4!J 3y, oAB: , * o. lIf 1-r.0. 3'+1-t<0. xt o"'=o;2x+r=o; e;a",,ia", l-1, o). L2 ) t1 !! Jr-2t oAs: ' + o. 51 1 5r l2.x -__2>Ua _>U. "f;'=o, r,-r=;, '=+ l s;anoaiao: (:: o) u lr: + - J. 6) { lsr-?. o.[B:.rr- lr" -1 x I r3-g x 2 -<U: (r 1Xx'+r.+1) r 1 ," 8 t" + 2x' t'+%c-t +2 (r 1)(r'?+t+1) I ;:;:.!:.$ ::::::::!l 1 2 2t+1_<{). gos. t, (* '3t' oi or3r ir r 2: x ' b. (x + 2(, 5l (r , 3)' 0i tr J). 0i -r. " J. (.r + 2Xx 5) BiAnoqiAb: F2, 5). z, tr*3f .0 (x+2)(x-5) (arr3. trorclleEEn ao saBAaHns 1). BiAnMiAb: e2,5r: -3].. B, ql?+ < o; oAB: .r. , + B. (x 3)" fr+z=o: [r=-2; l" s=o; l'=r. BiAnosidb: l-2;3) u (3; 51. +V1(-::V- 13 -i"'-; +Y-+a:])/'+ |E-2br r /--: ?.--/- ------.----+.---------.# z [el 5 ' + 3. 3)=0;rc=0:r=1ix=3. (jr + 2){x 5) ^---:------:i- = vi 311 ->ui at * 5 ^<oi o.&3: xt 2ix."-8.(x + 2(x 3)' ::_=o: j 5=0:.r=5. (x + 2J(x 3)' Bion%iab: ( 2; 3) u (3; 5). , '.,j ", 0:ir,-"r 6 0:.r--3:"r z.fl111C-(.r rJtir- f.r r i) Bidnosidb: l--, 3i '(l; 2|. 7, LaL.a, on}i x+Ii r+2. x-I .t 2 2 3 - 2tx-2 r3{r l)-4(r-lxx 2) ^ x-l x 2 - {r lx,r 2) z'__1_fL Q:4l1t2x -8 <o. 4-y'/r l7.r-15<0. 4-r?-17.r I l5 ,0. (.r lJ(n - 2) rjr l,lir - 2) {x - l)(x 2) 17+7 I - 4x2- 17x I t5=0:' 49: ',. =- ; , nr =1-i r Jr al' - r1)t" ar 4/ ,O. (r. lxir - 2) Bidnosiab: F*t t €(r ], z), ra, * -r. u 2-+4;>z: o1gtr* 1;'+-2. 2 3 ^ ^ 2lx t 2l -3lr I) 2l.r + l)(.r 2) ^ x-I r'2 (rrl)(r r2) 2x-4-3x 3-2J( -6x 4.n -2r"---!' 3,6, 41L,-3 ,6, lx JJlx t 2) (.ir - 1,{'( ' 2} l"r - l)lir ' 2) 2t'7rx-3 -.o:2!, x 4=otD 2si r,"=-l+5i t.=21 t" r,s. {x' IXr r 2) -- 2lx-1)lr.+1,5) -^ (r+1)(t+2) BiAnosiAb: C2t 1,51u (-1i 11. 494 lli: AITEEPA Mep3reK A. f, ra iH. aKaaeMiqHlrn piBeHb :a:a:;::i::::::;:i:::ii 11 4 6 l2x + l'ztx .3 e o: o.[3: x . oi ' t t. ,r"(r. + I)' ,.. frz'+rf =or ", ,= ];' f*-z=o: "=, " BioflosiAb: ( *; 1) u ( 1; 0) u [2; +-). 6) '".41"-g'o: oA3:.r'z 5r r6/oi,r,2rx t3 -4a'z+3t^. : :- 0; 'r1 - 4r' - 3.r = 0: r.(.r' 4xI r(r 1)(, 3) > 0. (x - 2(x 3l BiAnoqiob: t € (0; 1) u (2; 3) u (3; +-). g06.rrrr -stE- .o. oo". [z-t:o. l.z.2.x t3 [x/ -1.5: [.rr-1,5. r"-st"E-_r. r,, cr6: = o: 2x+3 ('-3Xr+3)J2 jl' >0. 2r+3 BiAnoqiAb: FB, -r,5); {2; 3}. x=!3;t-2. ,, rl;'$ a . o, ,, -,1,_fE . o, oo", {i I _1. rl-llitlr 3 o, r, rf,/i-3 = o, [' , -l' 16 r' lr=.3. (r+r)'rE+3.0. @ q@+4) BiAnwiAb: | 3; 4r. --a/1 z t,s z 3 x " (:(34.4 3 FI 4 -)€-]V-.10-t + 0t (t - 1r(t' + t + 1) + 0; t + 1. x' 8 r.r'-2x2+t'z 2t+x 2l .^ --- +Su;(r-1)(J'+x+1) (r 1)(ir' + .r + 1) (r+2X, 5)=0; (2r+1)'('-2 r'(r + 1)n i:l:ittiililiiitli AITEEPA Mep3reKA. r. ra iH. AKaaeMi,{Hri piBeHb r:::i: 495
  • 3, CreneHeBa OyHxqie 3) a=tlx-2) i D(a)tt-2>D; r>2tteL2i+6). a=t-2 q v-{a4;D(y):reR;y=lx-21. soz. 1) 4(-i6)' - t,.vm.o - [i ltto)' =-2O-6+40=14i = -20 0,6.10 + +.640 = 2) n[, -1".t; = "56- = 1n = t 1lJ2 - {12 2+2$ I,lltz + J2 = {:,z,fz = 3) 4) 5) 6) t, ,, srr. rr i/{z -.,F)- -,lz =lz-,111-,lt - "F - z-Jz 2i srz. t xF = d"" -" = "'tFzl v_a' = _i6".a = _a'16, il 1862*-j = 418L2*" *"."' "" = z*"oli^"o" t Et rls6;W = {ir a'- . ," . om = zry'{iz; s d-zney' - d-ar. sy1 - zy,!-zy: al ll."o" = :1"'" . ""W = o%,lo"r" . grg. rr 5= = 3@= -sE -stlz. v4 v4 .i/2 v8 . 2 ". 12 12.li tz.dz tz.tE ,,1.. '' E-ffi Ts--W - s -"'"' ,, g=94=s4=fia, 'V8 {az 2 ,, 14 14 V7 :.41,!i .xE. ! 4s { 4s.{7 7 ff'.fesf i,[rtu uI=t ,6s lJsb-d=z-.6b+JEs-e=r; = <F -,rlq;,tA = O -;AWn - F - txil = ira - -2. gog.ri s i/3"-sr D(y):3.r - 5'0, *>r3, 4 a= -t; D(Y)i-,>oi/'<o: '€ ( -;ol; 3 a = 4!x a: D@ri x e (-*; +-t 909. 2) 3) 4) 5) 6) 91o. u=llx-2); zl y=trG4; D(Vtte(--;+-): ,(r):re(--;+-); 12 relrrt+1: qt v {6, . lt Det.6x x, zoi xt6 -.r) z oi -:G/- - : -r-0; .r=6:.rc [0161. 0 6 rl .i6; = J"l = o, s*qo a > o; tltt =lo = -a, slcqo 6 < o; {zt*t*i =ls^^"'pl= s^'""p, 'Krqo n < 0; t,u"Jira"^ = t, t"lz"'l = -2,arn , snqo r 5 0; ,68"- =Uttl "b! b",.e*rqod-o,c<0. ah. abc abc 496 lll ATTEEPA Mep3rtKa. r, ra iH. a(a,qeMi'{Hrr piaenu il!*:ilfl*it'ii:'r ,' e. s(a*f) s(a*"El _ s(qtuF) _^*,r. 4 J7 14-h)14 th) 16 7 s .. r (Ve' {6'Vr) {6 -.f6_j[."' {a*{t (17tI -(q,E)' 5 z) ^ 6",_ o(a , zVt '.Vzr) o(l - z'6 . Vzr) zlr t z{s . <!zs): 2 ts 2, (r/t)" J g(S*r) e('6-r) e(t6*r) a(Vs 'r)'' plzs lt ' (Vrs - 16 - rX",,6 - r) (vb)',r, 6 - 3 ,Er ( :ittilft:r:*l: AII'EEPA MepsfleK A. f. ra iH. AKaaeMi.rHran pieenr ilil1 497
  • gra.u Wa =iE a =4,8; 3) nAG ='vc' . c ='d"'; 2' flE{t' = {t.'t" =:{t"; q 4e =lt = Jz; /, l(r;)"-,il=(r,_rl)(, _s))=2,_s =1 i_ r,!, or Isl (o.sq/o.i)"")lr,'" 1""",^,',J l':-i.,ll"l1',. "-l;l',]= [3r_(1]'j(s:.i;l l={,,r lIj] l' ,, ,, ( rl . ,n, l n',, , 1 t "'" " 1 ' ' l ' l { ni i,Er 'l [r: -titlll(r; -rl;)='"' f- tL""'e r I J'- '-'"' l- ' 2t 1'' ' - =(ri - "')(ri - r'") =(rl" - p-'t" = z - z' = z - ft= fi . n,n. ', i"' l a ll '- rg'r l 'i a: - s';'l ,u"J 7 e'ti, 27' | 3 33 125a'-h' t1tt "nrh, 256arh, !? I' I on. , ; AB) 'c' 625c'3 sl f6ri0 =,Sls='ne. =Je; al *lzJ, =42* =42" = *lr. gts. rl i6o . {6, .""i"'"" '6 = .Vsl; zt Jo . .,6, oc&iJlbru i6 = i6e ; Ji = rll%l al l/il r "6, ocrin*' ../5 = 16; q {n, 1E,.""i"'"" .'Ei = lF='itr, t/5 = i/d ='F. nru.,, Jg Jg_(+6-16)('6,' Va) _vo va. Va + Va (V" + Va) .. s[ z (J"-r) 1 Va a 1i7o - r;1go * 2l la +2 ^-tl^" <1,,t Hn | ., "- -_= :1-= !m = !mi Jn tn tlntln r) 4.lV +etli +s {V *e{" +s 1 x-27 = (G ;nV-, :V, +o) = if-, a' ! 9't7. 1) s = x6l, D(ar: x > o; 2) a=xa3t Dtlt: x oi 3) u=(r+ 6'6;D(A)i:r+6>0,t >-6; n€ [ 6; +-); 8) 494 4) y -(rz -6t-7)-6t D(y)t ? 6x-7>O;x= 1;t=7; re ( -; 1)u(7; +-). 918. 1) 31'. 3 o?.3' { = 3r'o' 1:!1 2l tl 3.11 4 .11r, .11 , = 1. 121 3) 360r'6-01=6'{.6 4r ::=a=3r =3i Ba Bt sy o,rzs i+o,sri-0,216-,? =1o,sy'+10,s)-'-(0,6)' =(1J'-(*)' (9'= ".10 25 ",2 l. I I 3 3. / .1-* r -rLo, (o,ozzlJ +zse'- lts'iJ =(0.3'r"^ 2so'5-ir=o.a 'z' l =19*64-1=3*64=62; uru""" -(.*"" t) ; * (V*)" - 6,y,, - ii . (roi)' - 5 - 1 + 101 = 14; " ,] l(,1)' , n-l llr",e,r; -(,;).J l(,1)'.,. ,= lll: lltrespl wtepsncKA. r. ra iH. AKaser,ri,{srr piee}tu ::llfilillili{li l"Ih: *"trb:]" l,ib;(,; .b;)l',,, ,jri , =l__;;,,r,lu;r'' ,,0, olo,, ,rr t ,1, ,t+ I o,b, I b, I b,ol +u) a-, a a)l-l- ,i, rtl a' ta!-aaba t a4a4 b1l) 92O, I) Cnpoqycvo,liBy qscrHdi roror+(Hocri: I I ' ' / , , I ^ , n -n, (n' m-n-n+n"n"ln' l;:;; ;.f,,)r^' ^,1^t,^),t (,'i_";)(,"r.":) I l= l '--' =m -nt n'+n') 11!l nL1 n1 = n1 _ nr. IoBeAerro. 2) Copouly.Mo riBy qacrnsy roroxEocri: otb a-b oi-bi oZ oa6t a6r aa + a,aba +ba aa bj t tl 2 r/ tr 2 I r/ r r la; _6,](a; _a,b; I b") 1,, a,ll,' ta,bs +bsl [,'_a"J(""*a"/ t,r - !M ,, _ ""t, _ o') o', I oibi bi) rr1111111!rr =at +bt _as +b3 _a3 bs =bt &3. br da =Da a3. AoBeAeEo. :::::i't:iilijf.!i! A'rEEPA Mep3nex A. f. ra iH. AKaAeMi,{Hlri piBeHb ii:::
  • 3) crporqy€Mo niBy 'racrlltlry rorornsocri: ).I s a3t2 lorr8d3 5 d3 - fd+8 o; 2j, -a) 1-oi r-ai 1l s aB -2 I as+z '';'"-;-t-n (,!ffi-; ,)-G" ,"i"1 31 ? - s-ad 4a3 -4 _ 5 - a:_:!as I a+8 a+8 t 2 ! . 5_as_4arl.a'@ '8t 5a. a_4a3 z'_'--l (a+s).(t-d'/ 1-at r oi -qotr s-oi sol -a aoi *r ,3 -rol . , s s,? ,,r I / 't'(r-oi]tr *,iJ r', o; h ",Jh-orJ r+03 5 = 5. AoBeaelro. 4) CnpotrIycMo "1iBy qacrusy rororkHocri: t ! / c ^' l',1-+ ''w^' ,l +', -,; I , l-i-". .J ,?.+nr ) , ';---n "^:,: (^i 'i)(qi ' ^:^I '^1 "^:^'"' ^i _^I "" " {,,r ,:) 1 I I / r I L I I '' n' * n;n" - n; s^i ni =l^" *2^'n; * ""1-14, - nll t t[ ! l]1 I ll 1l ,l' , , , , z zr' t , r ' 2 ln' +nx)tn'-n,ns +nsl_n:l ^, lni^;_ni n;l =n; _n;n'l = I (,t-,1) ) ,t . r' =n,m1 -n'l . It r' l-t -",t 1 1 1 -t. ffi= -,. ,. i lotelcno. ni ni -nz) gZ't. t J+t * m = t + 2; 4t + 20 = ,c2 + 4x+ 4: " -16= 0; (t 4)(t + 4)=0; lx,=a, Ii"peulpxa, ", = l, J+++m =++z;6-?,npalurbEo;r,--q, J-le+m =-q+z; 2 = -2, senpagr'Irl'Ho. BiAnosiA': 4. Z7 u6-i=Z'-t;6-t=gx'-24r+16i9x'-23x+ 10=0; D = 169: 23113 - 5 ",., = fS : xr= 2, x,= g. soo l{t ArrEsPA Mep3rcK A, r. ra iH, AxaaeMiqur4i piBexu llillii{illtN 2 = 2. flpaEhnbHo; x, = ;: 4+2r-x'-r' 4x+ 4;2x2 -6t= 0; 2r(r 3)=0; nepeBiprcai ,t = 2: 1Q - z = z z-l,; 77 - = --, llenpaBlrrEno, BiqnoaiAb:2. 4 '[G x "='-z; IlepeBip&a: rr =O: Ja+Z.O-O=O-2;2= 2, ls.e!pasuntiflo; z"=3: .lE+z s-s =z-z; 1= 1, rpalrrnbno. BiAnosiAb:8. q 1Er" - llt- tl = S - x: 2x2 - L4tt + 13 = 25 - 1Or + a2i 12 - 4t - 12 = O. nepeBipxa:,,= 2, ;a zy u.{-2)-13 =?: ? = ?. rlpsB nEsor x, = 6: rE.6"L4'6 +14=-1;1= 1, HeBpaBHnr,Ho. BiAnosiAb: -2. sr Jr-J''-ir =x-tr r-uG' I =x"-z*-t; '[7 -," =z* '" xt x?.4x2-4x6+f 5x,-4xx=O:.rr(5 4IJ - 0i.irr =0 a6o ,"=i=tti IlepeBiprc&: .r, = 0: 1= -1. senoalsftso: r.^ = 11, '4 f rs r i r.iI--=-: 16444 1 4' =0-1; BilnoerOt:1!. 4 6 'li+i-Jui =2t 'li+Lt=2+Js'+7; t+11=4+4Jiiii +sx+r: -2r = t1li7*; -r=Z,,Er+7; x, = 4(3t + 7li t, - 12x - 2A = Oi fiepeBipria: x,= -2t J-2+11-J-6+7=21 3 - 1 = 2a 2 = 2, npaBtrnEgo; ,"=tc: "Ea+11-Ja2-i -2; 5 7= 1; -2= 2, EerpasrnEgo. BiAnoqiAb: -2. 7),8 - % - s = J16 + x; ./l - zx =,lla+r + 3; 1 - 2r = 16 + r + 6li6 +.r- + 9; -za-zx 6,h6tx; S-r=2fi6-xr 64+ 16.r+r'?-4(16 r .r)i 64 l6x x, - 64 4x,, x, r 12x = O, x(x + l2t = 0; [x' = 0' lx" = -12 IlepeBipxa: x, = o: uii-zo-a= u/io*or I a 4t 2 - 4, HenpaBa,rr,Fo; :t " = -tzt,ET zi - s, = Jta - n; s - 3 = 2; 2 = 2, rpaBn.rbno. BiAnogiob: -I2. a1 ula-,+,1*-z=r; "6-i =t-"li z; s-t=r-zJt-2+x-2; 2Jr-2=22-4; ,Q-Z=r-Z; x 2 = xz - 4t + 4i t2 - 5t + 6 = Ot nepeBipxa: = 2. .tE - 2 + fE - 2 = 1; 1 = 1, npaBgnbHo; r, = s: .,6-+.v{_z = L 1 = 1, npanr.rnr,ao. BiA 6iAb: 2. B- i:r:::ilt!li:itlli: ATTEEPA Mep3rqKA. r. ra iH. AKaAeMirHrt pieenu ltl: SOr
  • sl "t x+5+"lt-=t: ,!z'+r=t '"b-t; 2x+5=16' }nE .r+a-r; ar rn - -8'6-; s,6 1 = 14 sq 64(s x) = 196 84r + 9x2; fg2 64x = lg' - 84;t + 9t2; qx'z 2Or + 4 = 0; D = 256i 20rt16 - 2 r,., = rs , x|= zi x2= -. repeBipKa: ,,=2. "E*+Jrz =4; 3 + 1=4;4 = 4, npaBlanr,Ho; s22-D lE-4{i 5=o; oA3: '>0. saMiga: V;=r, t>0't'z 4t -5=o;t,=lit,=5t I Ire 3a{oBonEEs€ vMoBv i,t .5; r 62s. Bi0no6iAb:625. zl Vi + r$[ 18: oA3:x2o Savisa: Vr =t, t2O.t'z +3, 1a=0; t'= 6it2=3t -6 Ee 3a.qoBonbg'e vMgBv r>0. 6t, o. -" 4. - - aro BiAnoqiAb:729. U "lV-q' ' q-z'J' 2-3=0r G-2)' 2t[x-2 3 o. 3arina: {t 2=r. ',t2t-3 O:tr= 3; //=1: +lr-z= e; x-2= 27;x= 25i ;J,-z =t; '-2= :':3. BiAnosiAb: 25:3. a) l=8 r.3aMiHa: Vx=r. i -u. 2+ -!x Lt" g_1 . t4 - i ) (2 r-r)(8 i '?) o. 2+i .--' 2+t t2+tn/'-r-6)_0. I{2 + 2+t l2+t ,tQ =g; x-o. -5neDeBiDXa: . 1=8 9: "=-1; l--1'npalurbHo 2+ J9 b o ,ffi .ffi.1=0. Bauisa: /tt =,, ''o' r 9+1=o; l+l-6-0. t,+t- 6=o; l';"="? t Heaa'*oBonl'snel.MoBv'>o; -rr3 xr3 4-r r12 3xt15----:- = 4 - =0; - -=0; x 3 .ir 3 x-3 rlepeBipka: ffi uffi.t=0, BiAnosiAb:5. u) .E ' ./f--: =1, o.qa: -L-0; -j-=0, I'=0 .rc(-*;-l)L{0; -).vlrr ri .r 2 I r xrl l.ir. -l: aa*i,,a: _E=r.r, o, _p=1.!1+r l r t ,r!-f,=o, 2* 5-t+2-o' zt'z-5t+2=oia=st r,." =tn?t r x-4-4x -Sr-4=4t =0: =u:1+r 1+' 1+r -32-4=O, 1+ r.+ 0l f r -t !1+r 2' 4x1x 3x1 -=0: -=u: 4(1 + r) 4(l + x) nanoaiat: -!; !. 7, ""-4,-,,8-4, 1=3. saMiHa: k -4'-=L t>o;x,-4r-1=t2t ? 4x=t2 + l:xl -l -r-3=0:1,- t-2=O:t|=-lit2=2. -1 ne 33,qoBonbH.se yMoBy t > 0. '[V - t, -t = z; x.' - 4x - 1 = 4; x' - 4x - 5 = 0; r. = -1; r" = 5. nepeBipria: 4 - -t; t a 4 - $ a 4 - 1 = 3; 3 = 3, trpaBr.rrbdoi r, = 5; 25 - 20 -,85 - 20 - 1= 3; 3 = 3, npaslrftso. BiAnosiAb: 5. , I a Jral lr Jra l 8) 5J.r?+3n-I=2x +6x+I: OA3: xL :r llrl 3a'riua: Jr' . Bx I = r, I : o; ,,., ar ', ut n', ") ), , ,'t l 2f+6t=2t2+2. 5t - 2t' + 2 + lt 2t' - 5t = 3 = O; D = 1; 5a1 r,=1,5, a lr,=rr uE+Sr-t=1A; st Jzz f +3x L=2,25;x'z+3x 3,25=OtD=22i vtt J' I t; ,r'2 r 3,r t = t;.r'-3,r -2=ot D =lF, *.^ = ttitt. ", 2 .^ 4!Jn s t "/itt'Iono6lob:-:---'-. 4. TpllroHoMerpxqHi OyHKr.tii 023. 1)cosr=a+4; -1 <a+_4<1; -5<a<-3;oe [-5; -3]; le" "" ro 2) sinr=6a-az-lo; I - =t' Uo o'z 10<1; a2+6a 11,<ot 16" d' l0 > li iri;iilliitl::;:tl: AITEEPA Mep3rqK A. r. ra iH. AKaAeMi.rHri piEeHb ttii 503 2 6.!2 J-3,r + 15 = 0, J,r = 5. l:r 3+0: lr+3. +1=0;0=0. I l. r. L"-r' f__ a l'- r' l,* t. ll l, = :'. 13"-r=0, L1+r+0r n1 12+tlt2-t 8+t'zl ^ -=u: 2+ t 'It =-2' rxi' r -6)=0. li'-i o o, ]l-' ". +O: t+-21 lt t -21 502 !!::: AnrEsPA Mep3ns( A. t ra iH. AKaaeMiqHrr piBeH" f;:ittii::,-f:i!li
  • a.z 6a+ 11.>Ot a!-6a+ 11 = 0; D=-8 < 0, seMa€ EopeEiB,4€ R' 6a a2 - g >O; -a2 + 60 - I > 0i a'z- 6a + I <o; (a - 3)'<o; a = 3. tae R- I - o=3. BiAnoqiAb: 3 . 924, 1) sin 168" cos 126'< 0, ocl{irbxtI sin 168" > 0; cos 126" < 0; 2) te 206".cos ( 223") < 0, ocliinblcs tg 206" > 0; cos (-223") < 0; 3) cos 4 tg 3 > 0, ocliirr,lca cos 4 > 0; tg 3 < 0. t; 925. ll sin?80'-sinl2 360"-60')" "in60'=;, 2) tg 900" = tg (180' 5 + 0') = te 0" = 0; 3t cosl2O0.=cos(360' 3+120") cosrzo' -cmeo"- -!: 4) ctE ( 585') = -ctg (180' 3 + 45') = -ctg 45'= -1; llr/trn.,65) cos6 = coslz,T 6J = cos -6 2, 6r "t,[ 1l^,)=-"i"[r r"-i] -",'l-;l-+ _1b) ,=- srnr; 6.) , = 1,5 cos r. 92a. l) 6inx 5;3].o.zo: t,ctg'x=J; .Lg:=t J8a 2 ' sin x dG lv,{Beprii crg.r 0i ctsx= .lg-t=-./g=-g.,l z0 lz5 5 Bionoeiat: -!.5 2) Lg(t=3i n.,r.3l; l-tg'o t, , "o.o=r.[z cos- d ir . tg" a I- rr€ III cueDri: cos r < o: cos.r-- /1 - ' !lOi stnc- lvr cos-ci smc<u; ",", = -.,f1 = - E = -: = -'J'.l 10 Y10 Jro r0 - s"toB tnoa th: -- . 10 929, 1 ) sinl o . cosi cr tg c = sin" c - cos:-qsjn a = sin' cr + cos'z c ein o = sin a(sin'a - cos'?a) = sin a; 2) cos'zd - ctg'dsina c "o"'o "oI19!lll9 = cos' c - cos' c sin' c = cos2 d(l sin'? d) - cos' s cos' c = cos' c; 3) (sin'?cr + ts'osin'zo)ctgcr = sin'?p(1+ tg?d;"rgo = 4{] "tgo=ts'zo ctss= 1-lsinfI+nos.rl': 4)--+=sln d cos d - cigd = 2ts' a. -""l,"r"--a-lI sin al 926. f(x + T) * l(.r T) * l(I). 927.llg--sil]'x+2i at r = coslr 2 5o4 ill: ATTEEPA MepsrrK A. r. ra iH. aKaaeMieHrar pieenr tiiiltliiill:iilil 93O. l) 2cos'?c-3sin!d. l-cos2a-;tl-cos2d) I cos2d 1.5, 1.5cos2o= =2,5cos2d 0,5;-1 <cos 2c[< 1;2,5<2,5cos2d<2,5; -B < 2,5cos 2c[ - 0,5 < 2. Hai6inblle - 2; EaiMeHrre - (-3). iitliiiillliii:| uresPA MepsrqK A. r. ra iH. AKaaeMiqHrafi piBeHb ::i::r 5o5 1- (1 + 2 sino cos d) -2sindcoso 2 sin'zc[ sin'd 1 cos0. - - - fr' 2)y=cosn-1;
  • 2) 4 cos'? Cl - tg d ctg cr - ocEinr'(r rarii sHartelrEs rle icEyloTl'. d*!+ .IJr.neZ "ta ctxfi+nn,nez' ^to cos(21r+cr)tg(n+(r) "-[" T) ctg,(sn o) - 1 r-r.i--i;(;."1 sina ctg 0 tg a ,. = "."" te" -' r-^l 1 ,l - tgd.tclg:d- l) "*[ie'c 'J -€ct{l -Lg o) tgcr -1.- {l- tg'o) "tgo 11 ts,ct. I (1 tg'd) tg'a tc(1 932. cos(s + ll) = cos ct. cos P - sin o sin 9; coso= .E-"t"""= n[-o'el = o'o; si" P = .'/i - co"' cr = u4:o,so = o,a; cos(c, + B) = -0,6 0,6 (-0,8) ' (-0'8) = -0,36 - 0'64 = -1' 933. 1) ctrpourvFMo niBv cacrl'IEv roroxRocri: r """a cogB sjnctsino(ctgd "tg0) sinasinUl;in" - "i"b.J = _ sin cr sin g(sin P cos ct 1 cos p sin d) = sin(cr + p); sin ct sin P e31. 1) sin(; d) + cos(n - o) + ic(+ + o) + ctgtt + crl = = cosc[ - cosd -ctgCl + ctgcl = 0; _ sindqosF + cosdsing = "i"(" * 9J = tg(o * p); cos cr cos B - sin C[ sin P cos(cr + 0) tg (0 + P) = te (ct + B). Aose,qeEo. I ^ 7r llt ) 934. lr cosa+sind=sinl;:-.t]tsino -zsrn4rosl4 - o.] zl "m(o * l) "i,,tn - ol. *"(". l) -<z' - d) = cos d sin c, - sin q cos o = 0; ciue'.J -1 _ -ctgCI 3) 4) sin !9d + P) = sin lq + 91. Aoeese.o. 2) CDporrvcMo niB) qacrxnv roror{socrr: '6 "o"o-z"osl l*oJ vz-"o-rl-"1""",r "r"|"r'"J ;{}, #"'* zl.r.i-""'"""1"*'l "o"''" fjglgl !9i-1 @-tL- -"- 'r , Jz "i"o - "gd; rs a = re d. .Iroseae'o. J2cosd' J2sinc{ J2sin<r J2costr ^. 2sindcosB -sin{o-p) - 2sinorosp sindcosp-co sinll - 't' cos(o - 0) 2sindsinP-ioscrcos0+sinosinp 2sinosinp tsn ) -"ielt "J 1- ig'(3?r - cr) =J2coslct-;l; r < """(" - l) < r,,/t < vE-"[" ]J..8. ""out"'*" ",,*""""' -'.8' 506 i:::::: A,rlrEEPA Mep3ncK A- r. ra iH. aKaAeMiqH,i piBeHb :::::::j:::::::i::j:::::;: 2) 10sin o Tcos q; a=10:b= 7, Ja +t" = Jtls: l0sind-7.osrr. | '"-sinc .'- "o.o .,/t+s Jl49 Jl49 ) = ,/i4g(sin a.os I - sin 9 cos cr1 = u/t49s;n1.r 11' -1 s sin(d a) < 1; -J149 < sin(a <p) < n4+g. na;oi.'rrme g"a'e"'o - ,{?-6. 935. lr sin2q = 2 sin d los (} = ts .., I + cos2fl 2 cos' cr 2) 1 cos 6c[ - cos 2cr + cos 4cl 2 sin' 3cr - 2sin3c{ sin (r ' 2sindcos2c, 2sindcos2d 2sin3a(sin3d sins) _ 2 sin q cos 2q 2sin30 . 2 sin (1cos 2d = 2 sin 3d; 6) 2sin0cos20 3) sin 6a tg 3& + 2 cos' 3d - 2 sin 3o cos 3e !4!q + 2 cos: 30 = cos3d =2sin3a+2cos'z3cl=2; 4) cos{ cr - sint o - cos 2([ + sin2 cr cos' o = =cos: cr(cos'?(1 + sin: o) - sin'zo + 2 sin'zs- 1= cos'z&+ sin'2o 1=0; 5t 2.os 2d + sin 2d --1 I - cos 4a + sin 2d I 1. sin 2d - sin' 2d +.nq' 2fr sin2d+.nq4d "-(T --).',"*,("-';)-, cos2d + 2cos'2.I 1 2cosgcr cos2ct + 1+ cos 4C, - 1 2 cos 3cr cos rx 7) 2 "." 'J" =-=cosq f cosa sinc) nos2c-cos6c (cosocos2a sin2dsinc').2sin4crsin2ct t"trrr "*rrl .lr'5r "lt- ".r""*r.2"t"r""".'i" - ros8o sin4d 2sin4ct 2sin4d ,. .os 2.r sin 2d.os 3d 2ein2.t.os2 "i*1" '' 8) sin'z 4.r - 1l 2) cos'4a cos' 4a lzn ) l:n ctcl , +za) +tel 2 - zct.] cos 2cr sin 2cr "nr2" "*2" 2cos3([ ^1 cos'/40.sin2scos20 'os 4(I 2sin2d'os2G cos40.sin4d 1. .- aos" 2ct sla" 2 cos4d 2 4--" --' lg2o. + clg2o. 5. TprroHoMerp14qHi piBHrHHr i HepiBHocri s36. rr "i"l{+I)+2=0,l6 r2,r xr r^_ 6 12 2 BiAnogiAb: 3,5n + 12nn, 2t 2cosl ! 1*,,6=o, 3 2) r5trr =+ + +zftn-nF/. 263 "r"f{.rl=-r; 1-.n, --znn,n c z; 6 r2l 6 12 2 r= 1 an 12nn,nLZ: x=-3,5r- l2nn, ncZ.2 neZ- "o.[ I 1l J:,: I ln l znn.n.z; 12 3,r 2 2 3 6/ 5fl 2n x=!a+ e +4nn.neL. Bidnoiidb: !! + ! + 4nn. n eZ. 33 ..:titii::ti:llitla AITEEPA Mep3ncK A. r. ra iH. AKaaeMi,rHrt piBeHh lr.l 507
  • 3) 3+Gicljr-;J =oi 1t 1l x= --+fin,n€Li x Biinoeilt -ft+ nn, n eZ. 41 4cte @r - 9) - 8 = 0; cte(3r 9 = 2; x=z+Iurcctez+T,nez Bi}noailt: 3 + larcct'e 2 + !, n e z / n r n -." 'reaz. sin[x ";)=;, , - =(-j) ;' n''nczr n = t: (-tt' [ -[+ n = -I-.:- " = ;. Bionoeiat: | . l,=!+znn.n,z, l, ; ,*.,-.. t-^t- L-"'=;, l, -^u*"!-zn*.x.2. znn, n eZ; t arccosl + 2nk, k eZ, /nrts i- l=--;" 4' Jg =--+fin,neL, nfi t--= 6+fin.nELi 4cosr' 3 = 0; BiAnMiAb: -+2 '=1-1yL-!r,nn,na7' e38. .osf r, - Tj = . "rO. * -+ t?! - 2nn. n cz; z, = -l' I - 2"". ^ ez., - =3{ t !. n"' " -zt 3n fi - -gr-8,I 1t ,=0,*.---3-u U = Zi Bianoeiat: ft e3e. w;= ; -;1nn'n-z: x -f,tznn nez: tt . 3rI ^ = ft*tn-U, n=1:rr= i-zlt-Ti n=zt x,' 2 2 BiAno^iAb: 2 Kopeai. 94O. 1) 2cos? r = Ssin x + 2i 2(1 - sjll2 t) - Asin t - 2 = 0; 2-'2siII't 3sin iu - 2 =O;2sin't + 3sir '= 0; sin n(2 sin t + 3) = 0; lsjn r = 0r ]x =nn,ncZt x.fln,ncZi lz"in*-a,0r lsin'=' l,s: Ixopeuie xeuae' hidnosiab:fin.n€2. 2) cos2t+sin jr=0;1 2 sin'? x + sin t = O; 2 sin' t - sin a 1= 0' SaMiEa: sin r = 1, t € [-1; 1]. 2t,-t-t=O.D=9i i =1: lsin.r=l: l,=" -znn,ntztl-3 ' | 2 i."=- ; I I I I ".,- t'lU=_U: l"i,x -r, l,=rtr,L, "x.*.2. Bianoliab ++znn,neZi l-r*tI+ nk' k ez' 3) 2cos2"t Scosx- 2 O,2(2cos'zx I) 3cosx -2=0i i.*'t -Z 3cos jr -2'O; 4cos -r-3cosx 0: cos n(4cos r- 3)=0; 5oB l{!l ATTEEPA MepsniKA' r. ra iH. AKaaeMi'{Hr4i piBexr ll:i{ii;ii:iiii;i 4) 2st 2, = tg t + clg x; OfiB; x+!+2nn,nEZi ,+fih,keZ. 2sin2y=llri+!9!J; z"inz, "in'':j9{l ; 2sin2x. 2- ; cos,r srnx .1n2r 2sin^2'-2 2s:tn'?2t-2=o: 11-cos4ir-2 0, l"os4x t: sin2x " lsln2x*0: l2x ' nt,teZ: x.!!.Lz: lax n 2nm.n-zt l.=I-Y,^,2; 2 l)42 l,*.t.zt 1_,tl -"1^= 2" '' Bianoeiad: f,+,nez. 5) 3 tg', 8cos'zr+ 1=0; OA3: x+f,+nn,neZ. ate,r-j._+1-o:- 1+ tg'.r 3tg'zr + 3tgi r 8+ l+ Lg' x =0;1+ tg- r. Slga {-+ 4tg'x -7 = o: arga r + 4Lg, x 7 o, r+Dg-.r SaMiEa: tg" = t, t>O.3t, + 4t:7 = 0; ) = 100; [r. = t, -4+lo t. 7 tt.z= O ilr^ 7. -t - Be ra4olonLu'c , 2 0: t' 3 f_ - tgx 1; x 'tnh'k-Z' n8"t=tt t"*=-1, : + fim. m.7- Bianoaiah: ': +'-Y: h c 7 42 6) 2 tgx rScrgJ.=5lO.ll3: x*tr -nn.n-Li x r fih, k.Z.2 saMiHa:tsx t; crs.r=l; zr+9-s o; 2!' -!i--2=ot [2" sr 'z=ot t t / li-0; ffr, - r,rr ,.- ,. lx=alrtst,l-nt,tez;I ltSx=I,b: lr'z-ri lLg'=r; x n tnm.net. lr+ft - L 4 Bidnolilb: ar.tg t,S nt,I.Z: I-nm,m.t.4 7) sin r + 2 cos r = 0: tg t + 2=O; Lg x= 2; x= -erctg 2 +nn, ne Z, BiAnosiAb: arctq 2 + nn, n e Z. " Ssin? r sin-rcosx 2cos':xdl Jsfn x, srn x cos ,r = z cos; xi ,-F-. =0;cos- J iiii:ilii{lilll: AITEEPA Mep3rrK A. r. ra iH. AKaaeMi,{Hxi pisexu Itl SO9 3r --9=arctg2+fin,neZi 't!:4.il.:l_. :::::Urlg!,
  • 13) sin r + sin 5r- = 0; 2 sin 3r cos 2r = 0; lsin3x=0. lz'=nn'n"' l,' T.,.t' Lcos2r=o; lz,. |. o*.*.2; L,=X.V.u.r. i:':{.!-::.i:i u,, lr=r: frs,r= r l'=n +nn.nez: r'.,= a i l, _2.l---_2. I'- 6 f/,=;; lrcr=i, l,=**"?"-^o.u.r. 3lg"+tgt-2=O. gaMifiai tg n = t. 3t2 + t - 2 = 0t D = 25i I . rlb f,, ?, fr"'- z l'-a'ctez-nn',-ez'r"- 4 ' I o I o I " 1,,=-t; ltgx=-r; la=-anp,t?.7.'14 Bilnoaida: arcLe?-nn,ncZ: -fr + nh, h eZ. 9 2,5sr'l 2, sin, r= 2; 5sin r cos r sinrr- 2(sine:r + cosr.r) =0: - 3sin'zr 5 sin.rcos.r 2cos'-r -USIn''f + bsln I coa ,r - ZCOS/ .f, = U: " I -+-=O: rc, x -|tgx-2=o. cos'x 3aMiHa: tg x = l. 3t' 5tt2 O;D=ll Bilnoaioa: Y, n eZ; itt, n.z. 14) 2-sin'z:r + sin 3x sin r= l; 2 sinr, + B sinr - 4 sinrJ._ sin r_ 1= 0; -4 sin3r + 2 sin,r + 2 sin r=O;4sin3, 2 sin?.r- 2sin.t + 1=0. SaMiEa:sinr=r,rEt 1;11.4f - 2t, -2t+1=Oi ltlrt=rt 4.;-2. _2:+1=0i 0=0: I. at' zt" zt+rlt-) 4t _ 2r2 t_ 14( 2 - -- il+l -2t +1 Bdnoaidt: !.n=Zi l.t)" ! . trk.kcz. z4 t7) sin'z.r.cos?2,!+sin'3r--3: l-cos2r ' l+cos4_t. I cos6r 3 2' 2 ' 2 ' -n- i.3 cos 2.:!+ cos 4r - cos 6r= 3; cos 2, + cos 6, - cos4r= O; :iiilit:li:jllt; AITEEPA Mep3rex a. r. ra iH. AKaaeMi{Hrai pise6r i.:::i 5r r Bidnoeida: ! + nn, n e Z: arclp? r nk. h cZ. 4 "3 - 2x ^ x ,x -lul cos- - l.Dsrnr=l: cos'- -Jsrn cos - srn' - - cos' - = (r: '222222 .in"!+s'i"ico'X=o: L l =ftn,neLi Itel*a=0, z=2fin,nEZi tc|= -z lx=znn,neZt lx=-2arcts3!2flk,he7. iilnoaila: 2nn, n e Z; -2 arctgg + 2nk, k e Z. 11) 5 sin 2t - 2 sin r = 0; 10 sin r cos r - 2 sin r = 0; 2 sin r(5 cos r -1) - 0; ^ fx=rn,neZ, lx= nn,nez,lsrnr=u, I I lt"."r-t=0, 1"o", = t , I r = t "r""o" I + 2nk- h e z. 'lst5 Bi6ni'oai0o: nn, n e Z; larccos! + 2xk, h eZ, Bidnoeilo: ! 2 510 i::i: AIrEEPA Mep3rex A. f. ra iH. AxaAeMi,{Hran piaenr i::,i!!:i:ii:ii:i.;:11 l,i.I = o, sinfl *nj+3.".{l=0, | 2 2 2 2' 'l"i,r-r-"|-o; [x=2nn,neZ:, lf,= - arctc} + nh. k ez; 2l=0; lx ( ,z "x'( ,x ,.r) "." t-"'' 2i stnzx. lcos---s'n-rJlcor2 +s'n' 2Jt =cos; l;2sinrcosr cosr=0; cosr(2sinr- 1)=0; f- lcos.r= 0, lr =a+ rll, rez, o, l"i.'= ]; I x = r_tf ! + na.eez,. ' -l 6 + nn, n ezt (-tl'E+ftk,hez. 12') si^2t =
  • 4=xm; *=2m. aianoaiaa: lfi+!, nezt +,kez. 941. Lg(5 cos .r) = 0t 5 cos x = fin, n e Zi "o"" = ]nr.rezr r =larccost*2nh,heZ.55 Bilnoailt : ! arccos4 + zfik. h e z. 5 942. sin rl= 2 sin r + cos r. 1) cos r > 0; 2fin < x < ft + zrn, n e Z: sin a = 2 sin r + cos r; sin r + cos r = 0; tg"r+ I -0:tg-r ti t=-!+nn.nez.4 3anoBo,r6gse sin x > 0 : x=4+nh.kcz.4 -sinr=2sinr+cosri Ssinr+cosr=0; 3 tgr+ 1=0; l1tsr = --: r=-arctg-+nn-ne/. 1 SaaoBorLsr. sin x. 0; .t = - arctg : + ,rs, s F Z. I zfi - arcLg; 2 cos 4-r cos 2r - cos 4x = o: cos 4x(2 cos 2x-1)=ot [:""n1=o:' 2aB2a 1= -n "*te| .tt 943. ltsin3x> 2 i t znn <3x <8 + zxn, n ez; 44 n 2nn fl 2fin 12 3 4 3 ln 2ftn ^ 2nn Bino'idb: l'r+ ;t ; + 7- l. n e z. Ylrr5]I- , .or;< ;'';. ^,. ;' -;' 2nn' n ezi 2! n 4nn . , .!! r 4nn, n .7. 3U t ,n 101! ) Bidosidb: l';' - annt; + 4rn l. n ' 7' s) "i"(,-i) < +; -! * z^,s,,i=!+ 2,1n, n e7'i - t - ! * "", t " I - L + 2tn' n ez; -ff+znn<x<$+znn,nez. nianoeia,.: | ff , znn; {t+ znn)' , . z' "'! + '' =znn<zx='lr-) -2nn,ne7t 3630 -L * znn < 2x <1! + 2nn, n ez; 26 n3n -;+r,n<x<lr+fln.neL- Bidno'iab: ! + n4 #+ nn ). n ez 'h t x [ fr -nn.n-lt5) rcl;F;ls:t, z,nn'i '3'6 """ -' ,t! * "".a < !+nn,nez; 63tt -2! + snn < x < -! + 3nn, n e z. 22 -1 Bidnolidh: | "i' + 3nn: ')+}nn],ncz' ZL) o, *"1 ?-'-ll >-t: nn.4 !:3!,nn.n,z,b L * nn .?! 3!r i! a nn, n a7i 554a t 2x 19n +nn<-<-+fin,n€L' 5521) 19r , fi+'fin<2xt-+'fln.nELi r::::iitili::iiti: MTEEPA Mep3rcK A' r' ra iH' AKaAeMi'{Hxr piBeHb i!:i 513 l7Ycl ln l0M,! 4x =!-on.o, 2, l, =;-7.",,. l, =X,T.^.^ *"2, ], lr,=,i-rou.o,r, ), -;, ^o.u,r. Bidnosidb :- :-, n FZt !' | fth. k cZ. 846 18) cos'1 ,r + cos'z 4,r = cos? 2-r t- cos? 8xi l+cos2r l+cos8r l.cos4-r Ircos6t 2 - , = 2 -- 2 ' 2+ cos2t+ co68r= 2 + cos 4r + cos 6r; 2 cos 5r cos 3r = 2 cos 5.! cos 5t(cos 3t - cos t) = 0; 2 cos 5r sin 2r sin r = 0i .lnnnl r lr=-+--nc7- lcossr 0- Itx=-!ILn,ncL, | 10 5 ll'lah- lsin2r=0. l2x=nk.hez. , i.,u.r.I sinx = O: lr=nm-mez: lr=m,mcZ. 0; BiAno6iAb: Eane)xaft IOi 2nl, sfi v a a 512 lll: AITEEPA Mep3rer< A. r. ra iH. AKaaeMi,{Hxi piaerb l{::iittalij:iii
  • n .nn 19n 5xn 2282 n :JnD 19n :inn Brtnardt, i - .n 7.': 2 8 2i 944. I' ,o. .,r,cos'3 Iar.s,' /3 "n"t I , I n : 2 2 o 23 6 2r sit.,r.sir', ".".n"' "i,,r f,t -,"'t-r,3:63: ' I ./l tl r 3r rs 2,r 'r4 i. .c zi, ^l ...,, l : ,r it in ;,r 1).a 3j'r'."s : 'i" 3 - 0 ctC 6 "tC " "tA r 945. l)a=nrcsilr(.r 5); t!x 5:li4<i<6; 1)(a): [4;6]: 2) u = arccos (n! 15); 1 ! xr 15 < 1; ]r' 15.1, ljr' ! 16, l'' - r; : -rr '"' : t+; ,tqr: [-r; -,]rJl!,1"r.r; a ; 3) V .arr,tgu/y1 2i r + 2 >0: r> 946. 1) q 2ar(sin:r- 1, -X:"*"r"r'.ii -n:2arcsinj.!r; 5n - n 3n t5n3n r2,rc,r!r. I l:l.ttl 141"44 2) , . 5 3 rrcctg 2.r; i) . urcctg l}- r; 37r ' ;l arcctg 2.r ': 0i 5 3ir . 5 3 arrctg 2 ' 5i t(y): (1, 3ri 5). q47 lr.rr,.",r= ll: Y- "1 l! /,, Rr,ln,ntnt,: Y 2 ::r ar,r:r, 5n. tt,r",,it i, :lt : 6ill s,1l=0.21 l 2 ,i l4 .i 1.1 2i D(ul. | 2; t*). ll2n ;Jl arccnsl t 1) . i Bidnoair)r: ]. 2 .r1 arctg(:r +.1:)- |: :. r J; = *, . = 4*!, ' = '11 ltan'nutr: ! - I