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MAIU Zea f.i* lcxl bcrt€-S
,T f 01a^+ -,*t a*\"ot olnt^,{s lrl4*lo^rs / 6,*,o cr.t{uo d.c_.
ct
1;$6rr.*$.1 eTr@\z,as ^\\o^: L^,8 tD qpr*, *trn.-
*. ,+ J^'qe "[ ay 0,* ?**bt. aF.,;r. exc*r<gi_c,
leaal,l Ue^rrnA\ g.d i^; 4p \rA lD ; ?,,^+ p^rr,e-{e ,
A=RA,,J\^"r" ^ rB +t- a.Gelr+rs,>n
"( 4-*- .wbok rA rrltlh'[* h,tatss / a^d\ t is -W -(*rua]d
\Jr hrlo.^: "-!*o.{ A is N,^- wW *+-h* r^o\oi\ , v,, rr:\taL \tset/ r3 -l^u rakel. .,-tLa
T6d"r4 ) ;a . ,lt"r-re$f"
,LLtsrt\t:.
.{ otry
A Ft:: *r;t,
w" Ju^ trle aN{P..rc*Lr,.-ba^ ,,:rt *iwo- "rl,-f1r 4"A"b ", )' o.-rY, v5.L, ft=8,
An,(L"{ekr, f' : tvlA rg -h*- Sarr.,e ,?s :
rt,t
o Me F fnV F hrra. € S
b"tk V*L = f qrd, rttfi = :F are
,$
La{: \ dcn$rdar F,rh^ r\ a. a.^rhdl n ^i"ta{Urns,|
f*r161
'\1',o^r, f = -,"g, *r\*re C u\ # accQ-kva;,lr',,^ ci,ue
+b (fo",q. 4*;, & ei,^r1 t.4* lo'.
d'* .. I
W:,xFA,We h*r,s ho.1 Jo. ,^.lq1a,s ,.*}e. :
r,/: i: & -:'-N :: --gL+ ce cK a.
\),2 hr3 it\<6r^le owee w.use
pLLb) :: -*.n tt n cL + Tg
.^r\*. ts r! *-[* da^,Ktqret- ,
-\ -Mot c A^/ B wq ,va i&l rdr{ib{ ,.,ilror;r'grc,v:Ae
^,As\€d sa,r\<rc1- h l,'-tbu**l q}lraoripw,
fi,flaq r s{ffe 't4 ,W "prt-t ap r\ o.l.
re*,["J\t 4-- o . .'"h.] l*ttr \^S J.*\ ̂{ :
rc F) : o ^^d L te: -i: /(ol ,j:_ 6,
t €*\, vs *Xt t c . so t'(o) := o
-:L'^ , 2('' ''^L-* B, 50 )cLo) ;g+- 1B= o .rlIf^, ,-^ t ---i"-;-u] lZonbtl\
hrtqk,J \^ re"\ , ^ f^,l$..'c'\€ ep-rre-c"5 "de As ,t(, 6'it:
fr q"r) ^rfu\ o-|: -"{tos dwq N { ag&,ua..n- 4*+ l'*,UA'rs qF odd,a1 *ftc.n yrph".t -t" Vz. h .{hq c}ax, 61,\
be-""* " mV ;: *.rnq+ hVr r k.., co.gt, ()\k d** how-.-fu*- {rorl {b C; -{r*q ,{e.q hvt
\,re Cau ,ryaf6*rc &* Slt*&J_S!*l_q. ,,--ilnu. ir.o_O ,'^J,\,.c'
-t(ou, \ r/ro c",le "t a'@- r-,o i = o. .*[{^e,
vov,c'$ ^! *:\^*h 'h{r qcc-urs s c^[*o{ i-r"e
t l@ , *d, 6 {'.*d lonrs\virr (!l ,"-)\*. i<){\ie' *y=, ry\nhv:r*c
,i\"{e V-r; \-px*i*-\ veLni\ R -f".^d,\, ,-d€ t,,"t
rq+d*iF 3t?:$p,Y \e{iIt g1r9tY ( ri 't\eu'( c)\-,A
{* .h* {*rnhr^ \W) E o, ra\nbru o-+ -b^- -6**,,^1r\ C rrr.
^ On,bD H" * dn-,Lri #-,* r\ i -l a,@) # - a.€),1 :: {rte,
fJ . {1* q14let -.[ 4"* c["n Ts (1
) {1"" oIE K [4--{ D€otr,ue ntr/,\ ,1 "|L<: Wrwt
,l.t*r( o^ po"er. " f .1
T L'3 l', @)- ,
or iks;^g\
,\A
C{enva{i,-€!
tA n r,o \+' *f-'= o , Il^o^^ )We t0 4'* Ai&\ ctq- i,n
Ovr q-\, A^b -\t^- olE
5r Lr,u,^n }rM c'DEs
"/
shnt .^r#{ \u*^*', Rvtt 6w-1er o g?T. .* \ L.e,rL . .it(avtr
,*M: ?rd, "*l h5f^f6H g2^e kel p"l*t ,e(
"\qn *,il b' ,'^t{k * ln+nr uo\r,,,^ wavro*\t*"r fir6\ o,tdnr eLs o,c{ iDDs *{ t!*
)D4 A t\J J- I \lorraoqgyco.\9,w.*4*-+**\l..-+@-_,-, 6e^s{ar,* Ca44, (vst owV h"ar,r ou
{\xne o\(Q- CDts .+ 41,* er*,
^b+ b1 = c ur\^$q *ea,,*#t,{r, otW**h"^. -*.,, SVwL, 3, \-.{.)€- o4dern ''-{r,\{
t' = $H', C'=$b' eF'
L\,'= s\".ri \rb c,.^/t wr,k :
q+ h"1 r O , wL"re k.- b,h.
CDE i-S l4,"rW^@l!
Q*('-*ff(4,r'^o* ,W*Jr( r"'*#t &.''vsd ,
Wo *l\Cr qrrd
r aSt,e*ltZ7r
COv.rSilgf
At'\'/ '
<lenebl
J \^J\*^, k=-\ i 'rDe ottoin l'=-.t \*c,r /s=N), ,
('':es'"i*
-{**+ -lt^,. fo[f*^ ,\ WrL dt{-*t"h* e{pa^,,,1^a | €r,.',l,r,,
€{P00 , or l,* .ex},*r*{ of fr* nura}n{ e, ,y.c.8 .
.fu*.{ :) - e' so\wS '{ (
- r L'N(, XFO.:
;: g .rF = $t , ^A iE
o\- ?c.1{,at^r s,r[,.Lion+-'
11o*rq^"&, f\ s ^* +r-* ,ga"an vt st*tDl , Si^e-
g.*,r,\ &*Jtrr, r+ -1.^n- 4o^ q@) = Au*, i* jrcrr,4.a &ugt2,-i
,A , "*n >(*ho*s.
*A " G Y" ().ot- A coxq!*.,d- ^l
'n(,
t Ar\.bo tuzvVq"n
ory;/*( \r.^e-c,r,
c*Sh^nh "+
tODt h"'trf,"tt?lrMd$4.,
ttva"gl^*\S u,rrg
a
A* {a,ro 1a.\
tsd [oLrr y'l: l,,i
fq*Ye-
itc-
fut**^,* A, Lre ,@sl,
\+ \(gt :- qo ui^*eud\19i Y Ae-o E A = {nd-' a1
s\q t l{U) * {o t',\-J UR*^.h^
' An n-'h
a. bssdflri{ or*/rt,n
l.= C t, "1t^,^ UJP- pfl*rt
=) A =U. l;c) i1^,+
--Gc+pr-t -.r*-)h,i-tJ-'-'i
ro,\^ &Ao,L*rc^^*o{o r\ **kt^t^
( ,\^-r\r-*\ o,r b*datj *,rtl,hou. (:rC*
| , 1,e- >Lh* ,Ntz,l- AoL" *t* h.s P.- olE
* -To Cer*.",*xr"dte- ' t,^l Ao* 's 'lq. 3er,,ert(
,+)o ,.pA.-\ tlr^r ,,ll*l fle=lr"*
( W\pe
'i? z" JN k)"-s J
uol fqo i3c,IT
$,r, l+,4*l'ct-r-v'v t
/
t!,lh*t ^.br* Ol^n*\ W
]"d .Iv- exy f**hrt ..d[l
5)h^e- 6lC$^!ktnt,
reda^abb lo tjp, lt-zrrv*
l* vTvL^^/ \^1" S\ar€ *,f?.
c^,n qorn btu, ''tt*"{-
C.-Ju" 1{*l nna{
l-h rg
1*^
.l>- o,,^fu* 4^.#f -{-.- r ^*+ a*,
.
a^r\ :t .,r^rte/s\"*a ,n^r"rC\ i{s "nah>^
.o r.r. ilg")
.,
D$ r* A,n#.- e,,,-r ,#" { . j. A,,Al"o"li
'"i["i^,,M tr^^o&li%r B u,r,t'hr" *t^cl.\ as
'DL{J= -P , L, sru,e- t- ^"+b^ -fgr.
'i\^*, ',-.\)Q- h^r^{-,
. 4^o- o\ti- I b*tfl." t .-F.o, so ,1).= o
rf a sohbn (4"^q\ qA .t*.qanor.,\ oUrhir). \
,Arv eE r( b"- i"P -1<.*_ d&""Arf "rprrror.br T: ,*
). Yl vv\ +"" *^^e4- ""11...t t- d[ {},..r*hru"g ,i),C, , r),.k1
c-^A Alt (or^,{ !\nts 0{. ^^0L V {^ra l,urt,.r_ .,
b[qt,r bil; " r\b$,] ,. b\Q;
&'L;-t*,w- l*'-t aicF) do?a"A; rL r$
-\ finr+Y-#d{
i*rt -D bn- o \*^a,-r
n F--
-tr,^*.hr,*^ \@) 15Q,
^
e5g,,nw,^,\'^q- -|
, t__*c-
''l'*e- Cr^Jnir* tel .= /- 'B n* u5*,....{. n/n^ .r-l-
a\,.,Q4s,r,\h^J slgp,ttor -I).- # , ,t*."lDW.r #["^"1 = \(e^{ ) :: AJ
bg=,\1 .
| , { eleut ve,,\rxs / eEe,,*\*s ,+ ,^^,.[v*qj
*ssgNf
atu\-A,cbMce e
p\,Jt",""ttnt^l .,p-"|,*. -i"L* r, lt^,.
ftvr gynA'.ne*o,a n-f l) ,^;,"!'h
-
'f't*q
ikIeI'> €r5
is kat"lu"aal v"^tuVr*,ifd f t ,fr ,
as G,n 45a-tJ ae^t GJr*un \e*,^r 'fLnr,t
n,\q\-a,,"^orhtiarot qy \. yrn*arrn r\ eAUL"td 'f\\ |
Jbfr^;{r^ ,1" a,,\- obE A^"8 J:P.'
I)o lye-
O rrl.Jdt
r\\tR{ s
r\ !\J
',)l u)g
'\i't?Ytw,,A-l l^a^^
-. tJ, (i.x\ '.t-I \ -*,'}U
Lel''t
iJ'* Ol=" o r{r.14 eC
UC) ,=Jo.
{5 ,["" e-Ue g6r) -- e]'( .
^;! * [;];= tu"rq) du
"'. soln I f At k.= o
(t*ut;:' C
[s,l^*- nio*n)
li* oD'lt ,s Jurc-c{,n1
e\tl, )o 1 l^ *- S.: l?t r.L
,i til "'o
'\,''--lR.
{lQnarav\ .Sott^/i6", \r:ff%-n ..- P,lt/ \e. So n"e-
'iL'* Bc l(A*:\* -+ /f *qo
r,\rD It13*,, - k'r (-) "
l=nry*"
,A= L* .*r,\o( \r) =-
fi\r . \
7 e- 3".
€(r. - IY\tr) = 2.* e*' GRTPH
3 L"L ae$, R*i oat*. 6Dl5-*:&.r,4+4dr.{,-.
| ,lTax" .{r,riro- -tl-a -Arr^,
I'h k3= Peo
We "r'llr crr^ader Vc,rnav€. -F€o , -f*.'-ui[e -D|,$, = C'n
h1, sa ''lr'."-F ht-
Observuubirn
ccn"l^at esl Lci:'S,"\
sE r\ b\,11 '=-i-'
S*n* 4h-t U* C"*jn* 1f,6.1 S^hs["*U,,t\1.^\ \L$nt,= -P. -[L*nn
fvv" Y *\{ " t*
Aao Ao ,c- R^d l^.- an;"A Eola,[ru.n?U
:ft*- St- r s.
r.t"*r[- tutrrfn4
t
-5* At' 4=
"tgq5 1p-t-
\tlde 4^*l- r*|ihc- -0. "'l'u.- l.'r5e".eo"lr (a&., r.r.,c
Ie b5 A. cdrtst-aaruf , Srt4ce "
"to rA\+ :: A{,1 u kgr)
"p L^bAs 4= r)Solu"-t l-"-t? AEl
(auvol nu\\t5.D4-t -::
c^A sb Ag
fir",r.r*., f$ tUG> iS ^. su[,.rh>^ h l-'. [O{*e}q?*\\n , \hr$'--o, 'h^*
U,o)." t5e) t frrrr) e:\**-rt. ot
, \[Io-\,.\ F Ptgil ]\$\ **,i*]il=\-\O
n
\^ 4^g 6rsr,
&*b^"t A}\euc*, -lu'
'\Gq t Qu @) tQ 0,
3,*^ 4* tsC p'=1[, uu4 g4-
we h^*r .'hJ df,&) = ,tie*h", 6.su,*.
t
fbco n Aa'o
a*C- S" ,fi,"f"--
te)' fu*t
.l
W{"1 qt.h '[oV\An "Rcc
..^N4t1e- )
@ !10(!\./
tAt'l"L'-e- Soln i{i I
*lz<.
;3 tlbtt' tfr ::(r'
f nG), ^Ai()"-$pc"t) &
t fldegeJF '?.ov,pleA
h^^+ ,*,r4 &-,tvt t"a gpq p^,^Jt,r 11 l*,
t1"a# sr[,.a }|jo-l={', It^r^ \^{- .:lLif;.^ kesc[i;ltb.^-afd\nl tr*- -hu*{",.^u
qv*'v-J.al qoln $1,., l.-' f, 6rv,) .
r& u''ot* so6e,*l '\o N** a.r^ **b (l^, i\U i"i ',.^.t-
l** '\r* sa)^t 'b^u^.1 $tl^ aA $oA '"Wu;{"; ,,
t.rqx4? Y- r -r Y !
roe$. 't.
9\ve l' - [\ ="*B At s-^*e- 61nsFu^,t iS *J lt' .JJ,
) j't ^\d= :: oo$
-.,\nw.\f1" \f] + [It :: o+ R (. ==Td,
{} [..;BY'p :;,\ L\uur : "B/n
---il -.[t- lt-t-0,..r '- lqa-
1w)=(\\J
Txu(Xru"nte
S'\w q'tt {q =
- h"t
4 / $A:j6ttr + 2f,F'= c+ Lc ': +
{N $\n Nr
I .,/u,. -B-\pR ' \-d' r< l*
,'{t^n^ q {h =( , goYQ
ga O,L., ttr);:
$&r =
-"''iL*^^
Sa
t'\ nci(. t +\e
,) )r\ t.. - -d-*J'r +& ,
a^A "1&)==6 $4."+"a
t; :- :r*nlli
c"o &. n "^.fo[
{r'\ filr r,r,l\ a<
,,d\^/;;
r?-(Ig*tk- d
l S\r,q i-\ = 2r, ."4 {0, -lo,
\(e C,J Lnor*\\ tl,= T.j* ,
'-il&*, t$O[Ip=Ettsh-c ts P*-.[l€*\\.,{-*]. f"l1-X"*,$s
arc gA j,t- {a*So, oK * ' E= o end ep-- L IIt
ul.,c{v \e nD dric* ,fl R "f.hgt} <,\1.*s
l!b\'vl , il tu h$t c\ c^^s\,.^Nt Jcr*^. \F.\,tr a*,'tr?h ukz;\q" u GE7^^xo^
) >f- .:t^dd, &\ [*,*r"*6,*+
C
f'*^, \dn\qs= Et k$*n c) = 2*, S],C= orrqf .
U)e
t*Qlvt CLtcsn- R
^h'a
6d{ * n?*\,
@r"*oft"*-' I
I\on€, f,Vc^t
's
\@)- frx
,*aurOb**--T-----
5l-i.* il'
n \J=1t: $?tr)-* B,c'u
Zxao e\e-F ....#-*\..-r
?--wx-'
"'W t
dc {l-
I ^uh*is^lrs'
KB=. LBthC '" b
11- "-^e( { G', -lJo
-[r'\ k L@ v"d,J
.)l*/R
*E)' '-?-fiL'= hL'
St[tAt*^ r g
-h<. {,
I-) {3'
=? C.*
.&='R2-
Illot\U
, an{
e-\i1' )
)"\-/2L/f
)3cL
"^AC*r-*D.
1t'*- q' t la^ = 7-d r ?-;.t-Ll o
-qf $\"**- Bt ' (knl)Ea*ttsSr\'** u'* ltul= sr,'r(3rQ a,^d,
tt"r=$,,r$ 'rt
d u ,t ==- ier ' fr \
rt, ri ti
,t?er: ": Bs''r Ft)' \-aa- r.'-ra \'thr -frn'^ble
t >hr/"\d. t"$*d''-bg fVt l = I3onG")t (- "s("d,
t.*,, qut[15 " 3B.ctgt 3cs,\t3d t k(gsi^Q,r)oc.d.i)(;' ( l' ;,*/e.)
e16
-z/,V" il'1* L7'P
,lt'l
'{ir 4t" b be*-t,A €" AJL5 uu)e
' W sN^(.3") , < 3c+ h.K =' 'L)yqq GW- c''1& ) ' 38*lrCt s o
ey^nl'e
o6
ce$&'
,-\llern, e + c... -ffi/a
o l---l-t R\5.' L
oc, B (* - l*) :? -1- .> B. -.e- :--
[ *1.-
o.^o\. C.' r'-'S- = -=i*__y,.€=t+k.
{-s\\ R/\\C
lz
D
6l tk'
r\ -C,\r( I 'i") -A.f*-4\1er + F \)iJ-
n '-'\oC
-lAn | '-4a.t aC*{iS o I A_ i
A,err,ar, $Fn"S;
?(.r-)=-lt, +
.E<ar"o\e-'--'44
S\ue Un
h3 =
-T.g tb,o = T3a:--a')c , .-1L,^^
l$ n )..jt, ,
'qt^r ltAs "\o \*VI h. sNg / \^)a ye:,_e. *oB + lq3 :-:- r + Tt * R:^
QxneNt..{1n*s d'@.,* *E .$ b=n \ -ft* B L,za,,*<
Rn-k€- ''Vo\ua ,
i5qll.\\A-D LBe
gl.n-w -\
*.l : #(su
kRt* i: o
*{ 'i) ,^:t{il, {i€ru
-t*) r kB€ -tw
v1b
)
F-'lnI tlIrrllI L'"+
t'JL,- t
ll .. aft\k5 {o 5at\e- 't^e ,"ry[i; (\n A*= bq (N\ e,r'Ve7hr a F R ,^J{^ Wm e-.w{.C
lfu'w r! sllft \ gtd'io4 , b.tt r..$.e t-r* to tla *nry-r-..orb.
%-Ot, "ltn ,E re\,*e,/ b "fto p*bl,u,",- o.ll
s.,5 n ff'V"" "* ik S$r*L-lq^-% (.suu h*"1
It s'c$^s roaa^qbb Ird e-l' s .s-[r,\,|. relqrr,*J[ { *
t'ilus
it,ur^,)
qtt \R{ = &-W. Vc &5 ,.,sta{ .l ^" [f^,z.'r*\ -0r^.,v0
'dnb = toD *-'ku'^^il ; *I*k ^h*,s, cq\\ed "1,* $ wfi/ J lqri-.l'r,^. J drr^"C ers" ,
I'$
-L)l f,- 3'
n'F" k'3 {bn + kg-* ,
; 1 cD e'-|"{- =' el['< ,\J
5o, g'Qo = -{- "^d !\ratl= sL.t C- , ^^d !c,/(\ w\,3f [,-l,,
(:c+C) €:hx . \r).\q- h*t- ,t-)e-ot U,;$f,g,\
\ So \^)e- cs^. s-^{- C = Q, o^ d l\^C ,9{-r.; -," ;r-4z F-{
,I / '\- \Jr('.
St^Cc- tt' " - \- ' n a-CJ ., ,v\\'(
n '\
{r.t ', c.kn{ a-C^uprAiC -t t ) ,
,o ,',.\, 4(rt= ,{ ULO * t\rr.(x) ::- X.&"
ltr + AO-
*
)
/\,2 EC J,n)=-*1o
ct 4 ) {o
[tr) = ,n-'ol n
?X:o,r,o\c.
fx"\A*e€ r-Sf\,*- ('* h .::
,r. f h" "eg ,J nw
t+
[21 r'Lx.Fy-"{dD( t,tr,u,r{r^* yft) = 2|r" .vu_-ct)r ,
r' :]r '- lt--"-tir- "t IJ\r),iU
Ll
!ri0id.l -.tL hv\ i^,C1^ Fri- 1;1= ll-,
V
{ 61-[ .t 11 \e=( #t [i--LtLJ [l ,
ln aB*^\ , MC b 4o d\^Q- '1lU..ef
-{<r-*\ c
Exa'npie
--) ): ^ 6,etio"o\ue ro"h, ,Tolope A pb?Js {a *a ttu B- (+)r $r. frVle,
Eoblr C- ",',fl^lkL o( b, # nr,.l*i T3. 1fu"
l tv"ef
--1, , /."1o u^rl.
!.€r-trrq- ,; ^(.o*1.)
inrti"l!, e=e> o.4
) #= -kna
d! h^a-re: l1n
A\^, r \'*lt RRb :-tA1 D
r\ IHont. 3ln |s
.<tlr\r\ -Pc(N.ttL"-arJl
tG),
d^Aka e
h,n*hn' . /,,,
I'-RAb T- t. .r.t\A^
b =o.
+t"Bb
*hne
"frt\d
Q=
I
Ae.- haG
h* a.tGk+ t
OK
-hof\-e-r ,\
leoa" 46.tpk) i5 Ae-heb
,s[nt tp(al -- R e.
k * h*b = - hoB*-hAb *8HlRs e"-h"L ** h^^o h*e
$, B(lqs- ho\ '- h*ao
)
k*'- h* ,
-\&tN<, Lk),-
.> bG)*
-(w^, blqso + o?
:Sc A != ed K *"d\) Dto = Uft ('e-h-t
Rs-h;\* t
bp6.)+ br.e)
-bo&- e- haf +
fu-h,q \-r
ISqff" ^ g*b6.\t de$ot hno.,r a6, \,l)* tvwe-
LGI " ho "
r r -- o(!r- hd k\reu=FA\r \-- J'
9,, ,W rr.k b^ b* d^r"A b"^eA ox 4^(B{-,tl #-t1* "t* **h€s A "-/.-B.
(?n\-^/v CbEi
t A;l\e at(e T "+'[t^" €.^q&)f,'n be)$ * c|'l
Lr*} d\rab -fh.o*n[ A a&t "^A bv,av[r;
i- Fl1=:ft*:- , F= *, , {ur- ;if*,gbxnrr!qrr
In $J-.2, .^lL*, 'P6)- la= 6o^.sb, wq t'\nd.t *R$= {t"t. -\1"L L'HS @,\y\ te. *ri$ern r:r9 rq
yi -YnJ (.k \' -h{
) ,t_nr- \F 5) Q ,, \t'^cer
e &q\)'dh'[ #u* * eb*#l:: Rq+ U
-{^"&t*, eh^,'uk^H)'s R-,
I + f_no"j\' =: -efza-
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+ \0..,Y o"*l "w furA.
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