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Enas 194a Problem Set 3 Solutions

Enas 194a Problem Set 3 Solutions - il#S b'h'a r 6 T u yz...

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il, #S - b/'h'a,! 6 T,- u* yz- ?' rn- /y,, r) = | v' n" J = (sre-,) "r//*/' | "' s t'-*" I 6 y,,t yz=4/t) cu,(\,ryz\= It e.Ql , /- (-//) It '/t I O ,, = "'-' yz-^."n r ^r-l "nr? I L u . ( y r r y r ) ; l ' l : O I ef-l ,nu I @ , t: irt(tz) yz= ros // tl n/r) /v'r E t' "-'-' 7-1:' !!)l,t l':l:i[;ii':, f i a w d r - > o D yr= P0) - A4) yz= P/A, Ut*) h"(r,Ya)=f c 7 rUl / | = (r -al(r"5') - lr'--f' *if' J =\,*rA,-6r,- r ) *) = -cal (T/z* x) (€ *il( e.6') )r' * / " I z - 7/t\ ) - - \- ,6'* 6o'n tV' = z (FA'-O*')
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I @ z) y ' / - 2 f , 2 > o - c ' -si '-'s1 l > 4 , € t C z € 7'. garutl- f"za-c* . Y"= z;(c,"tr,.ru-t) - 7f,= O -? . c + Yt = fere'- Y r /o ): I L 7 = * f , I VJ=- s"r€ft Y z'bt= ( a ) = Q \ Y , = 3 c s:/ _s+ ) f c J - z ! , h ) : / t l: 2c, /-8c, 6ea la t,f*) r e - 4 sr'. 4 ( sr) a 2 - f , . - * 6 = o G - z ) ( r - 3 ) * c = - ? , 3 Y,(c:)=/ y//"):o J J . l = e r t c z O = z c , r 0 e 2 - Z ( | : C t * c a ) -2 = cZ ,ch \ e,_:J a r d y , , / o ) = o T 9(<, - ..\ Cr -Cz - t/z 2t' - 1 f c / ' / 1 = L z c2=_.r/to _- \___z < > cr: t/ta QJ y'/ - fy, *6y__a __ y ^ c r 2 " / n " 2 . 7 * y'r Z.tezr*3""ob* .r .*_ z."h I V z ( o ) = o J, O = o t * & Z L 4 =-tL ,4 | = C r r C z O = u z = I c r : * l lv*
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a r..)y/ + r, "z r = f l , e a 1- 41Q- V - cr €t'** craQ)- v/. C aru",* | ec2s"z* y,/o) = / 7i b) =a d , L l = c t r c u e = - Q ( t = Y = a v" -(., O=. c, C t = a ) * , / ttt. 5) 2ltzl tur trr 4, * f"cz c t +az) A - t 2 fj -D 3 + ? - + 9 = ? * 3 7* o.eols^t oenn / /{-. Hd) 12 =6 DePE.,:.t6EMT r, r 4t I Y, o \ = L f c z - c L / / 7z Yz( -'r 3 cz(ez.q) + cz= ", b,_t) c t = / - C Z = ( r , _ r r ) _ =/-?\ -r,# /r,\ rzr- d-", (;",)u * (rrn)e- o v) ro5- I t / = ?,a, + g cz -"+ l.='?,az+ Dc, + c.z: ( r"^l)-t= _ = ( r, - rrt'uq * * ( "" - a>Ey' 3 (/,/3)'l r I l l , 5 / * A : Iz*rrt at*6,| l z s l = 6 / - r t z ' 6 + - 3) ,:-'/=
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c ) l z t * 1 1 ? t f I l= 6/-/tZ-6/ = lZ Tnaaet^/asl"7 l z s r \ r r ) l a t " u c t t a l I " c l = c q l * a \ I = c-l ^<J *a (p.oip,u€h/*,u/) ") I a p[+l t b 0G) c !/t) r J.rrl 7-+tD€?Eat aFrt/7 I lae'rr)r 6;h) cf tr+1 ,r A,rr) | = " j' Pt + 4 Frt', 6.A
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