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Chap 09-solutions-ex-9-3-method

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  • 3. ~ - v v . ‘ '_.., ' . .z‘- » @ <78‘ -I-#3 7, - ('><.L~+i3 *1) db“ .w»1 m,<, 5 wt .-»M@ Fuf YV-:: /‘:6 w>~'~5@»® ‘ ...‘ '.¢'»~- '- " * -»_.-' _. . '=.'.". _ . _. LR ,' > '"" §‘ / " 7‘ -' ~' . "OF? (>5) >6. ~11 '91:¢_'/ +~1 )<JM. 7‘ - . L 7Q ‘ L ~ ~ 1» 3 ".5 #3 (")'(..I ‘F ‘xi’! 4 I >J4L ' A.-2 3- :1 >v1~~"/ ‘L . l+'>LA_.)l' =’ Q/r ‘ L (. ' ':'§‘f.f:?. /- _::‘ ' ~‘ - m _f=... ... . .~-.. - --- . "-,,__‘-A-..,.‘~-~---—-~-—-4~—§~‘~v.-_;.‘:-I ~ 1:‘ r 2 ,_ . ' ' -~ ___.-* _ ~ — —— i i 7*-' '" __,..,_.. ‘k { » s " . ‘DLQ7 Eva P -'__ .=,;<.’- . Y $'._ '8/+ lxi"! __. ]_;-.;'_M_._--—-(@ ‘ " '56 ah‘ . ' " <1/K F ' 1 '56) “ 1-,; ‘”°é?,(l34~ M g;i_1,<1.><>:i 27* V V ’° - QJNX Jv ' =% X A, ?~dM_.: ‘(1+sv)_~/ J; ,/1“ '-1gm :_. 121:5», 3' ; 4. , _ ‘N MW Z 1% - H.1 3I'¢Lv -'1 > ($1-”-‘— "““"“’“‘° .< -1- Qm¢“+c~ K 1 ' 'fa-~/ Y: ' -~ -H»/' A .- 1% 4’. IV :.- X >~r~"‘1 ; __ _Q_W,(.,.Q,,,g_ (£4)/x§~4._3»;/1-7) in ' Q./(:+v) . - L ___»- _‘ . j X e-.-~-a ( -.1‘ - . ‘__’_-:3 7L—~ Jr“ __(.I...J’_(, 0 ~ ~ <1»;. '1-.4; 1’ )¢;’3¢L 13‘. - . 0,.;(r+/1) = ¢”‘C" Q” 3 =- C . ~ 1'35 ‘I -' ,. 4. 1-: C »: . Q L! 1; I1;.w ._ - ~.-' E ""37 ' 2.». , ~’_ ~ " “Z-" I " (1-*%7'I =4 i " . ' .‘» - ,9 ~ ‘I —-* &»»~'.».w»w vn . I i 7t ' v AN #@' L - -.§7<_"4_~; 1.. 1- 7(_+ :1 C’ » =_.4/<§'?(' 1% §%1~ 37“ ~ L L- _ . , ' 1.. , .,._L (_CX)7( -.ww® ,1-"'3'X/'>('*‘i7.*' j ___,,../-’~' * % 2» Y .<‘ lI_v.. ‘I Y n-1 <9-i.-.*/» ___; __,-,1 Q/»>+¢ ‘ <?""~,,¢-W" /+7U%k " 5:.“ 2:: ,.{.}-2;/4'V ._~. J3. *¢r;,+<‘*,,~ )“‘~* ., +__X I _v____.h . ‘_1,;.._ .§(H_/)1. .-_ _.7(,...-_-"‘ W3 ~ " La/+|) " * 1 Q» §+ C CA 5/ __’_-_"'_-’_’________._>( P‘ 4 i ; _ "_l-- :1 K 1 I 4 =:| 1| F ~ : I » '4 Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin Page 3 of 14 : Available at MathCity.org Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin
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  • 6. . ., - - ~ ____ 2- _‘,_..§-=-_":.‘_;~' ;..~-.--m; .'<'—**"""""5-1 .'W~»H_.M _?-.. .-»._ . _._; __, ---< -'7-'-"";t.“:‘.“_I.2,;'.'.;?_‘:_‘ ..'.".l__-__..,.-- ‘~- , . '_.-W % 1’ ‘ ~ M~ (ri?~Y-/?1'5?)~‘~/ :0 ’ . - . u < ' ‘ u = 5' . . M ,.._% ,5;-/;¢;>@ HM » @ VA ' I/-* V _-= i/,’_(;T"‘_* °‘lY§" ? ' _ 2* A /7I1—“_7x'‘:vX r +53] III}; g!‘/l+v 4- [F-v ’ : 1+1<f';’.-;’L""_"@)’ 4,‘, /1'4:/.+/(l:_7 vx _1_/’;’_-*"-IY4-X :- _____--—-—'- .,-»-——-V (--» J 01'}-/-"V ' )""Y 'r Iva’ ‘_ _,_. ' A &.-v_}+,'L/1+V_/!"{ '. '1 ; (}+v)+U _¢ ?&;,~_"k&4_J/V . (H-V) --_(1~’) AA " =§ ‘='_¢;,~__-.11.-5.... . V é1~/ __-NJ“ .4 '- j(c,>"'f§€~)~ ‘ J» g _ <;¢»¢+*) f°~***@X_ = I-1- -_~-.» .!+—'7 7 vv% M, J QM} v=S~;~»< A/K. d~»<>»~* ‘ g F '__/ . Z4 V N». __0,,g;,§1+.)-= Iwvc‘ +2“ 0/v~{?;--$~':vc:"f')>"_“ K/“ax Lg-vf)+/:'-Vf ii‘ ‘~»":,'f.:*<‘.."-1,“. -¢_1M(n1V¥+»)=L""“ ___QM{l’:€€+9= (Lvc.x_ “§,;@@,mA -_ ~%</1;-+Q,*“¢” » 1.~$‘*.". I L“(/,@~.7%+a§___ 10» (Q9 ¢ <,:..»c¢>~!- -' “L-L "___.A-J /:6.j -; V X--7+1 , . % lg’ = <'/=~"-1‘%-+1 wk-M¢.=E A -————'-—-—------f,-o ~ » ’ . _ . ., ‘ . ...»¢-www-Inav-0-nnmnu-your .. 1 v‘-. 1-‘ ' .‘.~ .=.T_ ,_..:, "’ ‘T "3 . I-I.-—_-""" 1 | V 5 I .3, .£ . .IH s x Mk! V .,_ ‘.1 ' f ‘ V ' ~" -*" -1:3 — — — _-_-_--...._-..<- _. ' ,@.‘.-__ __.,..__, _._..7...__ —-_----—_ _ . __———— —_A~-.¢..u.¢_.v.. , M . ,»_' » T —£, ‘V '1'" _ ‘- » -- ~" "»'~~"1‘?"TT'f!1"§".W1'~""1t“L ---""'~vi I 1. . ~ ~ »- - » , > ~ - ' - m..~.. -.~._ . i ‘ >' ]__._-__, _--v.>»=su:m_‘ “> L7-f .~ - N Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin Page 6 of 14 : Available at MathCity.org Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin
  • 7. — . " . -,4 "_&.1;-_.=_‘_:;;; . ' I >_" '. . ; ‘ V’; 7 T __._-.. K-Q -*— ifj;;:.‘..". 5»~»- ~ ~ . V . ., ‘ '0. u , u - . . - ® ,~1o>=1 ’:r/2"-—*'-"69 ‘ .__. - ‘ _ "vi 'f..-p -. ; , ~ . »» - =1‘ n - :' '_ - ~ :_ ~~— :___ , ' ' W Q; -~-~' r‘ ~o ', $5, ~ “S “l .1‘ r. ‘-1 f.-.A ._ >:‘*i ; ' !'r‘f-- _ ., 1,‘-,. . I ' ~- »~. ; V % ,9, "m.% kx (M J/V _....__.___ '" W)3“ ‘Marni *3; org ‘W3 _,___;_ f,£_ 'nd waths ‘ »1+u_l_¢_/ =1 ? Lag‘; /((5%/),v __._; "f"f,’_:E°_.,1.a~, 7(- V /A 3 <1M~/~+~¢ _-_; avnk-FC. >9 % -_-1<~>==* ? A ._ ,1 J_":_'__QN‘{+Q _ ll ; .‘»1"eLo s " '3'@ ' ' Mana aw ’< _ ~ >1 vxv-I V 3. = 'XQ-x-I-'*( =>‘~{L’m+JA”° ___,';(_d/~1 -.-I-'-0 _) ‘,f(¥);‘o . <*Y.=.~.~/+/$3177 **#‘2€' 0_ p,,§—~; = vi g.../-Y ——€D /+>wl_;“i -»———-—'6D . u<v1-38-.@ ~./+xc1$/ —.= ‘VY Q1; X % ‘..,._<1~*= £1 W533?6 § _<_‘_-M;{"/ ._~_ Qvvx +6 _ - - ¢~ :- 4 I :1 <H(;§§»),1A == '><.oL*/ ,--—-"'75&-,“'Cj_'(;.>,l'/.»v1+C‘ ,‘. S.~;K‘(§’Y-Q = QMx 13> u(%+)T:g;) = QM /ml»; L~ “ - X L. *1» j-;. V4. f,';f,€ _;_,/ .=; ;+F¢+,* =w <11 / L . - / vc I_.: - '11.‘-I-7’-f . r -: v()=-0 % -1 4;-K'¢g.)=1~m-_ i —§ -~ _,_; Q a ,_%' Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin Page 7 of 14 : Available at MathCity.org Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin
  • 8. , ,.__l _ Y _ __.‘ . , ._ . _. ‘. . - -~> ‘.., ~~“,-~~ .» ‘ -( I . - 1“ ~ " ',,»_ my .+. ’ 'Q~.gy_-Lyn . V ' ~ ,_ . - ‘ - . ¢- ‘ ’~5*“§“Y”€“' ' " . ' -' ".* 3» '-vii -’~>. '~ . I ‘.., ‘. .- ' ,_‘ - I ' 4 ' 1 -,_ , V, , » .*. ,L_§;;-,.~ - s §£”‘< ‘"_ % m “' {7”?@@§m@p ~kw ~ -~.1 ‘I ,_ __,’_ -.= 0 7] := A~ " A £’i~!<*” V‘ "1 . = -(2.X~5.‘I>-4* -~ . ' * V _ - H115 '~ * ? 4»-1 ‘UwM_i-.%A%éj‘ % a_-._- .4 ‘__ _ u@@@@@"1 A ; 4x% 511/1 1-(‘>4-" % i“&’ ¢ “‘»5v~£>_v /£LT§5% _ .. v. ,_- , , 1 4»! V-,¢¢l"=='._/_':t,!-1’; %é% 22 w~ jliw ¢ =»rj;_.fih. V 1‘:.~v—1- » . . {-,,,,1;.'.-»-.. . Q,,_x;.»9 rs, P~¢»"»~lF"4“*” 5,1 -5. +.c~. 1@» ~J% MWQWWLY ~»~»@@»* A‘ »~=A~@*“° V L .2 Jr!-:= ‘ ”l,_."_‘. ' v+L°°"> Va‘-L ia»/A _% --] X »< _.= wigV l»| .'‘H“"> ' N“""( ' "T,) I 14 . ., Z‘ ¢Q~L V ¢’ =?M,_‘,.)%_;YL|,,@+=->~= i‘ IEETJ . ; ' . ::)' 0/v T?-g--" ‘N iv 1/‘A C7‘ ’ kI~‘ L“ L) av,‘ ‘ML - » Q/+1.) " £§;;;;' ‘ Liiafiw, ,1; . ‘ n ..| - L an ‘=9’ Y1‘! Q-1+2, *- ‘ - -P .. 1 :2 ' - -*i .- —-.-:_ ;:'_ |1- ]x:_ P“ J:;_1' =-i- ” __' ,~ , YfLX "Qt _7~_t1+z*> f’- ‘*9 L%§Z_11_§;___2_,< q:.1"‘ 4 ,4 '1..- . " 5 __, . _ -. - .-.¢...-.-M----n»--.-qgqaeea-.--.~wY""*' 7%‘ M D ii"= . , » 1 ~ .. » V '. ‘ <~x~jY‘| 3122"wMw;$w,»§i~§'1w1'4-mm A :.»".'v~;> __ ~ V - - l ~ -~ " - ax; I ..._._ ..a~_ »u,-1.¢¢,._ . ‘ ‘ --».--_---....._._. ‘ :- , 1_O¢iIv-f‘.-§— v*-‘-"Pw q '- * ‘ - - ‘ ., J. - A ~' -» ~ - ~ ~ - =»~"» mama:-nywwuzuua-v~:£u5;7';.m,i.a»r:¢...;~;;1¢m;;~',-¢,,_;_,$.- ;u_;,,.__.,...‘...;.. .‘_ _ Q‘ ,-_ - -~ ,‘ 1 ‘ ‘ I . . < W3 @ ’§'»;*>‘*T; ‘€ .‘., M f s vi 5 4 rm‘ ,, 55 ~‘. .0. _I QC’ ) iw X L. L‘? "i: ; .7 ii Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin Page 8 of 14 : Available at MathCity.org Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin
  • 9. .‘.... . ~ ~.»_.';'.?.§':':h~.a-."~..'-'. v __ ‘ - ,.' - ‘ ' >‘ -‘ . - _. . . ._ ' " _ _'_._1 A‘ ' ..-, ...»,..w-~>"" . ,-h A,‘ .; xx- . ‘ .: ' - @i@%xL+q.»qA¢s1*>J~ ~~<@»*~~1>@w =-== I *'@>=~"é K W."-¢wr>~ ' ‘ ‘?’;i"":»-.._ Q‘ -1 ~.*"4, '_ . '5' ‘ -#9‘, 1!-¥ .~.' _»= ~ ~ . 1"-1*‘ - :_A Q1?’-<~¢°U1 +51" 1+pr'§_(D ‘ » 1. V > W 6'»-f" P<,~1' L‘! == /1 £417 * ________.__--@ * .' .‘ ‘-=1z~l;‘.'I' . """“'3""'-‘T .,~ '¢.Lv ,_ .5; 50¢: @-,5-+qw_~;)J»; g (3»&+<n7+§~f)¢‘~ A ix urx’. =’ "5"" y ' 4 '4 "L", ‘ ~'::v.' fl: F: " ‘ ’ I Q ‘ ‘ '_‘"'.2>, ‘.~-1, -;= ‘vi _- ‘~ 3‘-,_¢ : -sq. ' -_-I-naf . _ ~ _._._¢...;.---_-¢-—-—-I"' “ """":'g‘I'35""—"'3 ' 5'13 ‘ W. " ' _' ' if ~_ ~ . ' ; »___. (LU U) ‘y‘ . : - 3% ,. »+»3;; 0 I7 ax am u»~5®@ ‘D L L ~J+x¢l/v .<.- 3'21, +q'1 — n 6%» 7% = ;%‘<§»__:.:i1:§Fl> -V ». 72‘(6+ UV " -..._ 2.+<1v+5~/ _6v - 6+Qv . :) V2-""3V +3 ~ ;.A 31$ 4-mv ._ _,"+sv+3 V - 1‘ =-. ' 1§<_>;./;*l*~' -= ji“-% 7 -../‘J-2>A‘1*3 2..Q,',,(/~““+~.'314-3) "=.—_) .a'~"* ‘L % . /2,~;Lv‘3.s/+3) = MC“ % A (_;f‘+1~I*>¢‘+3>> &"—f U **r.“:::f>.u., C. . » > 91; ".0 >1 1 Q‘/L>}3‘/ +9 -=7 6'“ ; * #-1.317?. "C “ -v s Q . ‘X- v_i_+_3L>:r_?-*1’ ~-u - ‘ ' . L Mum 1-“ Lax : X 3,.» -zra ax +3?“/*1'“/if- :.+_L + 3 L‘ '?_'"./.,¢ - 1' ,.- L 77- ._.f(L;;~4> 1 3*" /‘I ‘-' I .' .-'-1‘-I: ‘ . '.;‘,§>... e~1,+12.. '»- ‘1-/=--- ' 1* / -L 3 + Q T. w “<*t*fK‘H. _ E 13 * '“.L33 -.-. 1Q; =->LC-— 4: W, ’ »-_~=‘1?‘ -"0 5»- Y/, 7 k . 5’ Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin Page 9 of 14 : Available at MathCity.org Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin
  • 10. ‘. t. w _.- ii,i;¢gW'_;=¢=. '_7i""5""-~~'- - --_::aaa=:,-"'7 "’”"' "--"' ' 7 ’ 5 I ‘ , 0 .3 . ... .‘ 1 3! ‘ I _‘ » Lb . J .___ 4-bl +C— . 1¢bT,l~*b»-- 8% ._ girggjé ¢1_@»H»~§3»-~»-A”‘s%‘é7°’“?>°“"’1P“' % % J <A x+k J1:=d_7< I6.-<».-__.1-~. 3-;7+K]<->42$1v%* I>Z 5A;,;.J,--_'bb+*<- . ~~__ 5' .-1 V_ “T2 QL'=‘§i t°"'$°'Q"A" Pvrzgjjwry u~'1¢>J‘l“ “*9-.Ia:L; b)‘ MA L.’ 71 ‘7£'"l'$"' - .. 3 .. ~++I>5» X f,*—i7*% '+$‘7L ~¢°‘-” =~>< 221 4% ‘ ‘ .P~__X_}-P1) J-J :51 * ‘ K 5‘ U.-kuu H-(*3 ‘*5’:/ (I 33/ é x+;.+3W+§l"‘__- 4-h-K4’, % LV >43-l' -—(f§;+K>»"' M3 -3; -0 ‘ ‘ pc P*°"*'°”° ah »<-s #-_._l'--- ..==v ...---—---" M *><-v ‘ --*“-'j;;_"V * “ M 4 - w< °v _-=.1* PJ-Y ? A-.-=‘ t‘I‘>() ' 1 ' ‘ .3: 4' ' ‘ -.1: ED "_..: '."'7i-:‘._4' ' v ' ‘ *7 iw __ . 37‘ ; " /+>~<X7~< ' /~" _?jQ+';<*”"'J%g§,')'LJ“V g;%><+@>/%<, :I"’j("""5LJ’“ “ii?” dc-*J'7§’J' Q %/L74,- ~ 1 . _ V+'”o )<v ‘*7<*""7‘ ‘ 1 4.. ’ Zn .+@nc..-ax(H'Y) !""U+v) = 7‘ “ if ' __/ AU-4~ > :2 "VD A 1-9 —_;2~__ -.== Q»-(:+v) +9~17< +'Q""<°-' __v V 14 ,1y_A4/ A»-, _L ,_ QM‘; ><(;+v) J; "VL I+/, . ,_ »L __:£ncx(H.Y) .L * - --» V -( V >4 4, jtih :2? g“¢_ (x+Y). ; ‘~:> ];W¢ (1-2.+_y-VJ) " J 1 ;.4.~'*Q%-]>4.v.L—*==j@‘*-‘~ A 1-=-+1-I <‘T;"7_%¢"*") j >4 " ‘ =; -21-1-‘1 -_= @».é(=¢+_-1-';> 1 ._,,, -. ; 4. ,.--.. -.- ~- . .-. -,~- .- ‘)(.+_‘)-3 . " 5 - /'§”""""'v ' +79 i ___ Qt A 01-s -W -~ ‘“ '. ~~; ',i‘=.:§;~I/V "__ = 1‘ ,._...‘ ..._. -< ,___ ‘ _-__ .., '*'~- , . ‘ , k . _ , ,1 _ _ ”,-.,....--.._.....- ..,.....'..,»u,.....s;<- V-L~-':» -*‘-*"‘ ~ ““" """" ,i~,,,;.,,»_,,_.“,,,@___;_,. __; *- ~ -~-1-v -~w— *7 -~~ - ~ -11' V» - . __ - ' '- ~‘i..‘.....-.-¢.a'.-.=.»~....._ p-;»»»=u@C&:._ - .- ~ ,;;‘~ ,‘ ‘Y W X _‘ ‘ _. , J ,7». _ _, _ H < '~-'~'ié£'2~i'“""“ "‘ ‘ .|~.¢'.=.»i::.'.+. 1-L»-.s‘=-....»~,., -...-. - = - ‘ . . _¢- _ Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin Page 10 of 14 : Available at MathCity.org Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin
  • 11. mi ,3 “ ~( * ‘ L? (—'i: "_ J‘ ‘ff --nod--_:1__f’ '11-’ ."""-7'" "';”-""""' ~‘ M. ‘-*—:‘~l=v-1---4-;==iu'i§___= #1-L, *—===*====:*~»---4 '»__, ' . >, ,~»‘ " ' »~ ‘ ' ~._ .. -12 ‘ ‘ ' ‘I’?-f:'J ' . 'i~£_f‘ . ‘ - Ii 1‘ 0.. . , -‘> . ’> ' - ._ , '-,1_=;_,._. . -(Q1 +3j 4-If) NHDE1 _- ~ w 2.1+-3+7 _,;1?;’;_‘ a-._ '?1:'2;t"’>‘*/n; 43 ,_@v/ F 3 1 [+»< ix 3>< V . ' uh”; .b_ - ' 3: ...__Q< ><‘+¢/h+3>/*3‘K"'f52 -7q:u+iK+,?1 -<= E37?” ,><+:<;1+/+><+7 L @g;¢h_3x_';J,c° * ” ~ v Qh +.u<+1u==-= r 3% ,.- .., ~><~f>v ,:2>@ *'""""'-»<-I---OKJ ‘ ._ . I ‘ "'_________ ..-‘( _. .. ,_ ac ~P¢ (AL = ~/>4 49 L‘ 3QBL'°;% <29’ ._/-»@ .‘ 1;-;§,"=">{7A .4; v/JXOKR AW x= “ "¢»:~3@@¢..@ ‘- ? <=/+&><é’ =1 '" ‘1_>§_"_‘.§’.i3§~ *_ % M .:n<+/>< , fqkx“ 7((.:¢+/D . "F-_¢_<_;_~T>_l/_'ll/ii1' ‘ ‘ 2-+/ ><u l" =;~ L. _.~ ‘" : M4) M {_* M $ "éLyJ;2:2—_ g1)Ya,l.,~'1€b - ‘/4'1-_ .-_-_-__ iii =I_ +',... {g,_;-V_+q_ '§_,,,.)(v41-Q’ WI /#1 ?..v;-AYv4r<1 % j é /4-1.‘ / ;-_. A(/A14) +B(.V""> t 2- ‘ C,. °1"*"‘ . J” , - ',b,< Pu);-)4-RQO /¢~*Li'm * +2-J-~ __ . _3VK_k~J-r_x)_;f' *3 '.+‘i . » 0/"‘7<+QMC’ /+1=° /="" -'=? ....» ~.L (L. @+§) + >31. Mvw) = 5, '.' if-11 ~.= + 2' :9/+9 ‘.5 (W19 . 7' LVHXVH) 7' 1 ' . ' ‘A ,Z»n(€;£> % ‘~ 5 mm " ¢ ~ <y.;_@><_{ ¢1+‘<:_>£§ “_,? (,X?.)% X H , 74),/:>_€_"/:~_ C, ' + z,)(¢w¢+3+1;s3 -= c, ,4»,j V(.j§?_l;§jx+;3>(3+1+q1+¢§ ,_. G g? (“+3 A ’ >~»—-—/5" >‘ » . ' . . Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin Page 11 of 14 : Available at MathCity.org Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin
  • 12. ‘::._,.V »_--B3:-rgr > J» 7 V ~ ‘. » J at . _ 1 ~ ' V. v" ‘ ‘, _ .- ' - “ ‘ 33. v.‘Li>.:1;7><,~a.>d» +('7.'1-"3?"7>'l’7'O »<=~'"'*#*>~** ~ , . | .~ I’, .,;»,~,._ ~"‘1 . aqkb V V 2:11-"'9;4. D ;. >- ._pv~]; ,,_ ,_; 7(+11x in. . V 4-'Ih4'3“° §.{ 004 V-»-¢. +‘Hh+;u:'-0 + ’1L1+*<)*"°W ‘~" ’° , " =)(+-=f_ . PA-“!.» NW/, @ "pm . _3/74* /+ >$%e/1 ='=- , ‘ ‘ ' V (,3/1-V7) -V4 , V 7‘@"""'V 2 2. _/9.»/+7 .:zv¢2./ V N ‘ U dL7< 7<‘§’- ’ /$71? r~¢#>~'F~*‘*“ ~ .- 7( 5 f’" M Q; —2»:l/fll V ¢='-° L7‘/*37V‘_///{D 3 V (3 V’-" Q» A *"’_|' '7/'3 -=- ___,_.Z-- """' ;+/ _<i~J$' “F wl» M’, V -V I v-2 ¢ AL-">*'3° V _ 1. I’ 8~1P“F fie? 1 _._-.3-_ V/A I“:/> *3- »? 1 % V’ M [<.-;>‘§“"+5>S)* AQ’“°%% QPJL »‘=.'l . V -5 4 ”" "‘ ~/}V=fI$»<1>‘ 1-1 "’;>} Y ’@*£<>~¢;<1>“<’i%‘@1>‘]"“*’Z .- __ 3”‘ (X '2 5%’ 7< ' - P»! H/¢o . 1- . :1? I, 2 . @MU,,,)._0,,><¢ a PJ I V 7 C / 4: V .2. ,- ah 15' 4:» .- 2- Y v - ' = Q .§,:i‘f)_ Z *f,JVt'> --/( - J“ s ' ._v,_ - ‘ . ». e/' v!‘ 1 ;.-.-_ ' . ",4 _-),,.- M . __.___.¢_:_. __ __ ( ,_ .2» f V___ . I 4' ’ -qh’ ‘ | . , Add - , $ I I 1 1 ‘. 4 - ‘ .‘. '-- ,_. _' ‘. ' _ »- . ‘ - ... .‘ 4 v ' - ' -,..-~--~ ""' Q . ‘V ;~ ~‘.‘v’ - . .' " ' ‘ VV ’ I‘ “ .-4' ,- '- 3; . . V-V---—"'““" ' ‘ '.31~VV " 5‘§=’ * ' "N . '= 2- ..¢_v-V.»--~? V ' V -V; ‘- -» _ .. »-V"--iIII=4' _ _. -» ~=umu,_...A,._... .._.VV... _ 1.3. .‘ - . . ..,...., , ,,_,, ,... ‘ _ . ,_ V _. I . _ ____ . ‘_ . _ M, , V..,. . ' ~ . _,;;~,, ,..V~ ~~»Au w ~ * '_ .,, , V V ~ ' ,< . _ - -.- _:__ ‘ .. ~V.- .VV-1 V- V _¢~..-‘W ._‘._ ~,m~r - ‘V . . Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin Page 12 of 14 : Available at MathCity.org Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin
  • 13. r~_ ~. ~ ‘ ‘, v ""**§1;§¥ ;. _=v_~_1._._ 1 ‘ A I. -_ % j . ' 3 R ‘ ' ‘ Obi! —— - -17 +-5” /MOE all IF -BJ "(Q ___ X ~.- 7 Cy‘ b_ -H . 0&0 ,___..._--—--"" 1, J~ ~j 3;‘ A 2_'>< +11 — I ' ‘ t ?u-l‘(x».‘4==7<44'1 >00 cflti ‘A /. )<.|.I.,...lY';_2E_T‘;*i_ _ . Ix s ;L»><m+‘>’+1<~' A »3,, h_LK+&’° V _ ¢- z.b~+><“ '°° 4&1 =1 X_ly~ Hm; @ AM / "1 -4»<+1v=¢ 5" ‘radGLX »1><+ um -L=-1,+;4--:o *_________..--- A 'Pul"l’ .-= />4 __--j»-@ -——‘-""' "*“' V 0L‘/ A v Xdv '@ > G3:_.. L ==-" A + -—- *""‘"""' E£'><j 47‘ -- ;*=“/*1-L -~"~.~.®‘@v¢-an» % /+>‘<av =% >_§;-3.5113 .A% 1x+V* ; ~ ‘/D /Z;%5%>'/L ><A/A= m;/1i;.?~iIl’~. 2__/ (Q4-/» —;: """"""_'_ 1. ‘ 7‘ »,;~Qv—V . -2_-+/ ObJ.____-L -jél , §vL+W_, >< i . . ' »__QM Q//C» _A ,_ lA;;,,AL/’1u/#1)] ‘?' X | 1 - * v . F *-‘ mc‘ i gM(,+uv-1, V 7 J w “’1T§-, , :1» , ' . . _ 1 + ""'“-3".» .,j@,_ ' X.. xi» ' . -~-I . - , L ‘_5),;;,5»~~,‘ L- >< L ,_ J : "‘?1‘_+ (,1;-)C1' -34‘ 1* C" - "_'_ _ __ *},L::'-Q‘, Q-3,1) *%' 7 <1 ’> , . V --- X . " *_ a y Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin Page 13 of 14 : Available at MathCity.org Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin
  • 14. 1 t‘ .._-_=4|.¢|-'_'4a**>- —"'“'“ "' "'. , _n-..Li;Ll!!>l~ ---1'-— ms pf" 5 ' Q ‘ Nwpé Q‘ ,-E1 ‘.3-.f'1j’ - " 11%} 5,’; by > - L V " 2. ~~»® @ »J~*1 ,??11"*”'* " 51-1v~> 49 ‘@ 1;*:i~<9°:“"”"’*°7‘ ' v,-Z 2" . £5. 1'-‘WY Pwk‘51-“J '" q M‘ zitkz;x_ I31 . . , "| :- .; <F=f5!'»'A“z ’>4 _ 5 ab! --"""'@ t‘; ia .Zl .- @- ,_ 1+<£%~Q@ T71 . ;Qj .,~-_,@_~‘~<1>A‘ - . < 4’ dz) === g-"'2;_1_(3» 7! 2’-3 »_ -;- _ H ' ,. Q L‘2"-8‘ 612- ‘$- 3 %j,% $3 (Ii ~ dz — J" " "'27?Z14!‘ :»;;j;“i*i-*~’ ~43 2%;-_ZLi"l' ZUW 2+5 £7: z_+| ‘-2"‘? ;;;—$ 56* 2*’ *~r,~*‘°..~,W ;<~;-9 ¢ ‘*2 +95’ 7' JVXAMUs A? jg: , av A1 ‘*1"’“'}° , -.= -‘11‘*C- V i Q» j qM¢M ;§+>l . :2 __Q1*é.‘ ,_.d_'A Z-r/O7»‘_¢__,__ W1- Sal,“ _3,+2C. . ,_,, - "‘+/02»; ‘ /- S L 2- + C. 4-7», “-_H°@_»)+21= ‘-- 2); 1. €§">~“' " 5 + ‘ ‘ Z_qQ»<. i. 3-*-l»q> Q1_.@<)L+lo'/-11 =-'“ @»--»>~‘*°*““" ’ c S _ Q/_7Qv+IoQY-1) == ——.‘&vx SK‘! »,= ,¢*¢ .- D L‘!-v<)+_|=>‘1.~’°""”L " j :="’v£: ‘i , 1 W sf ' - 0 2 q 4 i 1 4 < 0 1 ) I 6 { 1» 2 '. . r '. z 3 i - B I Z T / 1 (.4 ‘ ¢_ _i ______,___--¢¢ M1 vuQ“(}+3“?”D’ K L41" ’ .’ ::-§_»__ ? L,wu*1‘>‘“>7 14 ~ Enlanaar 1»? r, V / ’ 1—%‘1> = CL Q-'_(*3 7 Mr‘ ” / »< AH iv.-~': -' ' ' __’____.,_ .7 ._?* " ¢__‘t._r;__".,:_g,;-¢_.. ~- ' .,_»,~g-..-0-"‘! .. """ "‘ . ~ H g‘_,=,,:_:_“'1.iQ:¢.A;e:»:1=o¢é"H-3-"‘5? .,____...4.¢.v,.<».<--»-~~->-::>:""Y""‘ 1,‘, _ _. , . - --~-~~*-‘-" _ - ‘av r _ ‘A 5 .»~--~ 7 ~-_-;_.:::'.';_;‘.:_' 1“ , ., ,., 1!{ -;.- <"‘ ‘ " ’ ' U - ,» __,< " "M I i i 4 4 1 -. [ 1 Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin Page 14 of 14 : Available at MathCity.org Exercise 9.3: Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin