taller

1. (1• ucir.°)S°3
(x quas)i_visoa -zy
(xic uastsoo)zuas = A .05
xji _quel x = •st,
- _x = (1x)uas -s¿
• •
I —
= 'EZ
(X SOD - X UDS 3),..,a = a -61
xr uasis- =
( rx ± )Das
(rata)ui = ri
,*9Z
) = *c:
'ZZ
=.8 I
OZ: ur1 +
oz, Das
(1 "9//' 'YzUDS t = 'LS
DI
c
e /va4
•ouasoo uppunj el eied uompe el neinuncij el dlualqo •(z) f anuanoua '1 + ny,= ( ni !S 15
v uas X SOD SOD x uas = (y + x)uas
~Te el op Eintung el xenuap iy (q)
-ouas uopunj el Bird DIL~OdSDI-103 EITIULTOJ U1 Eilualqo
alqop opbSue iap ouasoa lap emulo; ei Juis.pap Ey (e) -89
- x q - x v - x
(A-c-
+ rZ
ul —
=n
.9j7
1717
"Zt
'01
-1E
.9£
- Ex
x
I Mi./
anb a.psanwap - x)(q - x)(v - x) (x)f ts '19
•l aluaTuad auap aluaBuel ElDal
El apuop i = zÁz., zx asdpa el anos solund sol auuartaua -99
umuozpoti rloai run sa aula2uel
rl u!,-(-; () -x soo uas = muno ei ap sonind anb ua? •s9
•„. f Á ,l'f ap srage.r2 srt opuri
-rdwoa aiquuozri sa (e) oscaur lr eisandsai nsIs anbppaA (q)
l'U/ uas
„Y + ,x
C-
+ X")
- í= ,ax
uasDn)urpie =
=
11.
a.nuanoua -¿Av, > x > - UE1 - 17 = (x)f !s (e)
,f Á sensufs se! opurJ (.,.a)soo = *ZE
XitIDS - Xr,S00 = XZ SOD
-alma aiquuozei sa (u) ()spur lr elsandsai ns 7 anbppaA (p)
mued rausp.0 rl ua sal
-raSuel srloal sri Á muna el opurfnqw (q) os!aul la ansrui (D)
-(-17 -17) Á (z. ) solund sol ua x - gi•x
ruma ni u salualum SEPOI SE' Op sauopunpa aquanDug (q)
"(x),./ ziT11 - c/`1- = !S (r) *E9•
"soputuawo3 uleni
•-cluild ukts!ut ut LID ,J. f Pl-hcbG •(r) , apl.!„„,••?A- = (A-) !s
( '0) + Z) = '19
(1 'Z-) '£1 = + + '09
•roupazisa as anb olund ¡a
LID rAlna ri r leullou F, alualuri wuji salolarn3D JultuFf 19-89
so imu3r3
NOID'v'AD33C1 3G SV1D3'd £ 01r11.NEVI) Z97.
(x£ qsoa)ui = A -st
(zx)quas x =
L(£ + = S .117
- +
(O uas)zuel -6E
(Ex + I uel)uas = -LE
(g z.voloa 'SE
xc uri xg Das I ut = .c -EE
(rt)i _uel x = [E
(1 - x£)€(1 + xZ)
.0£ Auras - x uas Ul A .15-t-
+ Ex)
sco) = a -SZ (xZ. + 1)1101 = n *L1
= .17z, uas + 1 SOD
erg aso)uí = -91 .v = A..7 + „J'a-
( 1 - 1 4- .25
-
ua L'AinD v:i E PIUDIUU
( LO) t + I // '65
•oprp mund
ap sauopenoa a.nuanaug 6c-1C
(x- nos - .guas
1
'( 'ti
z(xz, uasair) = *¿
xu SOD = -01
= 't
SOO l• A = • I/ j
—
A- -6
oz,11:;,'d = •L
+
A./‘ G)
- X = A.
01[1310 09-1
(Z: + IZ - =
1•¿P
"t7
(a- tun)soa = r: -z
(ir,)um
• • al;! PpleAg • •cpg
Tra(u x) (x),„, f. SDDUalltD 've)A. = (1.).[ anb
gowap und (LL rtqlcd) rny,,ttiolutu u9pDnpu! rl anblicly
"(x - Z..)/1 = !s --111!m-la 179
I = ,yr 2J-•w-7.1113i:3 'ES
.(9/1),15 UOS R = Y3 !S 75

2. oiaPIP-'DA "11
osied -s cuapepiaA •E oiarrepiaA •1
OSIEJ-0.19prp.10A 9p segun; a.id
SI -
> 1 > O :Z < I (a) ot (P) £Z (o)
> o tz < 1 (q) = (i)v — ziE = (1)a (E) '68
[(Si + Jm)uas 019Z + (3 + .e»)so3 — r a)],,_ay = (1)v
'[(g "t'as (g ")soa d],„_ay— (1)4
x- + zx — = •sg
(0 'e —) 'es (t7)(rt, so3)(x17 uas),8((x1 'te
,[(1-)6 + (1-)f]
'6L (x)6Ax16
,:[(r)ax),6 + r[(x)61(x),./.
,?( ,d),B 'S L (1 ),b(-1)5Z •£1 (x),fizx + (1 )617,
olápepnA '6 osied "L
19Z VNIDVd w E 0101IdV3 130 OSVd3d
(ZP + I)uI) 'SS
n qsont, — n quas z = rC (q) •es
ovE.oc. (q) ZLS£'0 (u) '1S
I + t'/`x vp
I —
(£/x)i_quas — I)fZ —
c(x.LISOD + I _
= r),9aguas ( XrLIDDS
1717 (q) Z (e) '69 W— 'fi/1'0 '(/ 17/11) '59 (,a)quei (,a)zq3as ,az— = (1),f 'LE n quas nil.ai = -si
01-
01
01 (p)
8 ± =-. ± = (q) •
x£ — 01
x —• Z
(u) 'E9
Z+x = =
+ 17, = '65 £//"1" — 1 + =
uelpz;
iC/rxg— '£5 1— 15 '6P
(n)zuas u„,.,9(£u„, ,,1)11Ds £-
1 — rtitias /‘•
LP x£ 1-11-121(x LIMO)
R(£ ± X) I + XP
(z,s — rgs — — x) 11
(o uas)roas (o uas)uel 9 SO3 Z '6E
+ itz.
rx£
uul)soo .ze
. (S + Ex£),:3s3 x9— *S£ xSps S TE
(x17), _uei • ti x SOD x uas — X100 -61
z x9 I + I
ul (rZ + T)) I + (dx)soo x•LZ
(A7x)soz) A" — 1-17
z.-(T — X) — .£Z Ul '1)(£ U1).,„uvE
UOS ,.,a(rD
z0Z, +
I) -61 'LE•(1 — 0 -c; uel) oz 32S Z
—
'51KYZ — r.i — I (XZ Ovia
Z z( zi I)
•1 I '6. st'as — SOD
I + AY`
OZ S03Z: •1
(1 + Z)Z
LZP£ 1-PZ
(£ — zrZ)7(S + zx£ — x)x9 "I
17"
soppAah
x qum = (x), -tt x 1103 r = (x),f •ii
O (I) .7) (q) QQ (2)
1 (3) O M (p) <XI (3) I— (q) T (u) 'E/
x qsoo 'S = x x qoso = x quas = x goas
0 (q) 1 (E) *s
989z9-£ ~ ( z_a — (q) c(e) t I (q) (:) (u) •i
652 VNI9yd 53 I VE SODI311313
(dm °poi, (q) '8'17 (E) 'Et
(q) qi-EtZ (u) 'LE
810'0 1£U-ID 6LI z.111-179L I (q)
ZIO'0 t,11-13 LZ ^ 2/1178 (u) 'SE
%YO '900'0 `r1u3 9£ (q) %I '10'0 OLZ (u) •E£
S96.0 06/1/ — I V/ Z0'17 'Si 807;£ ti
szro— = = ti
8'0 = A:77 `17.9.0 ,CV '61
(q) rP zoos = ^P (u) • Ll
1010'0!TO*0 (q) = <CP (1) "S I
£(1:-1 + I) z(T n) -_tp = (q) np (u) ti
Z-
01
,x)quas (ér)gsoo ryz
3CI SOIDIMJ313 SVIS311dS31 I 3DICIN3dV tUl 9LV

3. E- = zE -F. - - E.IZ 'ZS = S 5UDS ± SI SO3 •-tc
-sp auFulaap `z1 X I c solopaafa soI ua
zi£_(dZ + zdS) = b "OS z = zbE - bdt
•bpldp aucrmapp `0$ Á 6{7 solopiala sol uH
x -
x + I
zA.
cn~ —
1.12S -I- 1 = a .9E
E( I - nt)si
= .0£
'95 (J) zuas z_x =
xs 103 ry = er .9z
,(1 x)oso =
uosx.A.z = .zz
z( _r_Az
1 + YZ)
= .Z£
I + zx-Z (x)2 179
I +
= (1)f '£9
-uotonnjap eI opuesn epeApap El aup.uialap `179 X Eg SOI3T3IDID SO1 ua
epenuap ap uopluplap el ap u9penldV
-(8 '8) olund Ta tia zap/e(,/, atnuualop '17 = ,/,(C E/Fi- ts 'Z9
-(i 'o) olund ¡a ua ,x--ppíj ap aojen la au-nuialap `x soo z =(1. ,((!s
= e + izO
tir(L + LO) = !s `0 = i no ip/jp ap .101" ta OTILL1010a
'(0/1.1. S')UDS g =
(Z -) nos = nt IS O = S' ua splinp ap .101EA la DUIUSIDIDG
«ui(nz + zn) =
is = s!s z = n ua np/sp ap aojen la auirunalaa
+ 51 = X XZ UDS E = ft. ts p = 1 tia ,ippCp ap Joren la ou!uualau
I = r(cx '9P I =d21/- '5P
'69 SI = odOI + sit,xS .1717 aL = - (C17 + c'Y TI7
Z = rc z1( + (Cr ± *Zt T = (C£+XZ+ (Cx'Ib
'85 -eEolidun ucgenuap aluetpaui xp atquualap `817 E 117 SOI0I01DrD SO1 ua
LS elpyidwl u9penpaa
'09
x soo
O = x .a
(x)f
I = x .3
= x 'Vil xy, -u
ap opep101EA ¡O
no saumoeuRwoo sawa!n2Is su' ap sepenriap selatuud se! auuulalau
S/ I £-
Z- 6 0
(x),.f (x)f
=XXO=XU0 SOJOJEA sal
-ua!n2ts sol uouan epenuap elawpd ns X (x)f umunj uf anb e2uodng
= x '((x)8 x)f
= x ziz((x)/ = x `((x)f ).5 -a
O = x 1((x)8)f 'P I = x (x)8.3
(x)f
= x `(x)z8(x)f = x `(x)g - (x)f9 -E
ap opep10IEA ID
ua sauotorUiiutoo saluatn2!s su' ap supenpap seiatupd sei au!tuialau
i7- z/T S E 1
z/I E — 1 1 0
(x),z (x),J. (x).? (x)f x
1= x ri 0= x ua saioren saniain2!s sol
nanap sepenyap selaux!id sns jI (x)8 `(x)f sauo!ounj se( anb e2uodng 'SS
sepenpap ap sonp.awnu saJoieA
- = za-ppQp anb ansonwap `oÑanq -y
= zic -q 1 = £A. + 11"- -E
:Rylandurr uopenpap 91u-omaní ,xppc_p DIUULIDJDa 'ES
E/I-(xE éc>0 + E) = (C. '01
0-(7 - xE)i,h(t. - rE)OZ = .8E
(i + 61/ + 0) UDS = 'OZ
O SOO OZ = .1 '81
(ziE + I - j) s3S3 = S "91
(.9 loa "pj
Z
X UDSX LIDS Z
x znas - xzuel z = jI -ITZ
.ZI
— ?A. iI
01 + - 5-6=
!/.
5(50 0 0S3 •8
Z
£(1 + 33S + ¿O) =
i_(X t)(c — = (c. .9 (XZ + zx)z( + = jI -S
(Z11 + ZX)1 1x = .1
tx £.0 + O - £ = d 'Z xSZ*0 + zxSZI.0 = ((-
'017 E I SOIOIOIDID SO1 ua SDTIOIDUT sud ap supenuap se! atuuualacr
sauopunj ap sepenpea
1 = x `(x),1 01 •
O = x '(x un S - I )f 'P
x `(x)f "ni
z/z(xz nos zz-s)
= '6£
I + xZA (I + xz) = 'LE
1 9 coi
0 UDS J — .9/
ZX
X + 5XP - .££
( 1:"^
1
z
+ )
- 'LE
( I +
- s '6Z117
(5XZ) ¡UDS 5X =j 'Lz
rxlon S = j 'SZ
z(x-Was = ((' -Ez
_x oso rx-z •Tz
uas = -6T
0 UDS 0Z/. = -Li
c(/ uEl + i oas) = s -si
(1z - vS00 = s • EI
•(f/x = IPPCP I +
anb ansarunap 'T = - zxap elmiduu uolo-enuap aluEipapy .179
XLJ... LX = •17
sepenuag :E o-in4Idej
9L

4. by + zdE bp
61dd1'– 179 = dp
£/te(17 xt1' + x
EP 'IP
Z + Kt7 — rxE— Z +
z(1 — o soo)
z( + x) ((z
L1'
x 'S1'
[zis(xz uas + zxg)]
6 6£xz soo xc
I + xZ/.£ LE
Bs/Pti 9/1– = 1/9/zOP `°°s/1)21 9/1 = TPOP (3)
20s/PEJ 59/8– = /PizeP `a3s/Pni S9/8 = IP/IOP (q)
Bas/IJ SL8.8— £1/_/Z1— (E) •£17
á‘11!u1/11!
'IP
2
sosipel I— (3) 23s/z$ 1•65_ (q) 205/11z7/13 0(EZS) :e Zz
aluapainap `2asituo £I/PI— (a)
anmsuoo `2as/uuo O (q) oluapán ‘Oasizinni7T (E)
y2 v _
ciP I
+ 41 0 uas q +
!13– o uas q
vp
—IP o soo qv Z = --1P (a)
OP I VP
y2
oo soo qv 12= izp_1 (q)
1
1;5/ osoo qv = (E)
zi( zr/- IP
xP x (q)
7/2 Zif
xP X = ST9 (E)
-6I
IP X 119 (3)
eip t xP
LI
•IZ
tu z‘f — /f9z/•. = (q)
Tul mo Z6171 = (q)
zupni7 1891 /9917 ua olimpo.°
2as/U II TE Tul/z13 u01' `e!w/13 1
unuim 1L'88Z = 1/9
S 'IP
ititZ
Illuita13 611 I =
2as/k1 00S — '6£ 23e/u1 S— •LE
'S£
*1£
(3)
(E) '6Z
(e) •LZ
Z—
+ 1Z)
T9 T 19 £/ '69 O •L9
17/£ (2)
Z/6 (3) Z1 (a) 17/1 (P) ZI /S (3) Z– (q) L (E) 'SS
I – i(zP 1711 – 1(zP
x zrp (q) = z179
"1)(1 — -/Z) =
gp
T9 „
"1
o uas z— •9£
Z11(
X -1-,)zn
I EG + x) El8
TE .1£ 6Z
1— x– r (I + i)—
(zx)tilos rz + (zrz) soo (xz) um cx8 -Lz ( x)r3S3 X0 I – .SZ
[Z--x Z(XZ) 91 lz(n) 035 z/IX-.1 .EZ
(-1)109 ez--) Oso + (–x OSO X
Z) °
1Z
9.Z/. 19 112S OZA
6I o uas + o SO0 e
,(1 Wel + i ogs) oas)c
(/z — 1) uas (iz — 1) Jon 8
+ I)1_/_ Z.
'6
•xy + i = (x)7 sa O = x ua uopuzpuaup El anb rogru2ls olsa
= (0),J anb ol aod _1(x + )3/ = (x),1 ‘sVaind I = (0).i
zI
y xT -u s— .6 rZ 'L
– x = (x)7 .s = (x)7 T £1 — xim = (r)7 'I
SLI–ELI *dd '6*£ u9P3aS
OZ/".SOO
'LI
'SI
xuEl x zOasZ •II
(O Wel O OOS OZ) z( + 9 005 + ze)E
+ X-17 ZXZ)(I X)Z .9
(Z X)X£ S •° XSZ.0 17XS "I
O81-9LI •dd 'enpead ap soppia[3
-rima ti ua pnnu2rin utuspn El ap oIcitueo un ap ()paja la
SDODA 6E ap lopapanu auap runi el ua pepanui2 vi u vino]) ucip
-uniaou El ua omtuuo un anb olloci Luí E italt sa UOZEI
%£ '617 %– •L17 %17 (q) °AZ, (E)
Eu1 9•S9S AP *£17 %Z (q)
zui 1180.0 (E)
1-P°-'- Z = AP '6£ x72 °xZI = SP
z°-¿-2117 = AP 'SE SI/1 (3) S/Z— (q) E/1— (E)
1E0 (3) Z (q) (E)
I y (3) - (q) 1 ti (u)
x
xp ((x"z – i)voo (z-A2 – 1) oso)
xp(1)70as (J•17)
ix -
xAz x KA.E
xp (x, S) so3 =1 Ez
17, z(zx + I)
•6I
xp
zxE) 'GT
zrZ — Z
£00.1 (q) 10.1 (E)
•nuatune X `las/sumo z/E (p)
1/9 I _ 1P I = 1P (3)
IP A AP ) 1 2113
,Sas/clum (q) 2asivion 1 (E)
y2 _az = 1p (3)
11P AP
—11-111-z
Jp
(q) — ruL = — (E) • £1
aP AP 11P AP
u /cut S£1– (q) Tui/zul()81— (E) -II ETRE '6
Z/E— 'L 9— '9 01 'E 5- = —1;-1p
£91.-091. *dd `8°E u91-330S
xplKp efp ifrZ £A. ,z1(1 £ zx xP
1 = xP ¿LIT + xP 1(X.Z + £1( e(P
(1- st
L
s
Z
– = tu (z— 'E)
_ w !—
a
= (z– `E– ) !
Z
– = (Z £–)
LZ LZ
'15
L£
'ES
'1£
'6Z
•LZ
'9Z
' IZ
'5I
£1_11,. ludan wawnu uoo soppiaca sol e sqsandsa8 :s op-p.IdeD