4411_hw4_solutions - 'rtDf4E uoqk 6.11 I T !')+' t I I lU...

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'rtDf4E uoqk o \ vrr 1L {r *----** I Fr -{ Lr' lO{+ : 110;" L.,lrGml; 6.11 I E,A,7 ' c,rtliTAr,\1 E= ZQ0oo rsl ft: tO,J;nz l= /1g;a'' 0 rRc,RRnn FoR 6,il , 6. n, 6.13 1..fiffiF L.= ll{-r = 2-D'1i" T t I l5 0+ I I I J T !')+' t I I lU +J I I I I -L ALl 'f LJ a At1 6 k- EI u- T 6,rt) l- Ar1 o o -t r?- 6L o 6u rlL" o ArrA!' '/ !7 .r -l? -61 o 6t T.?' o l3{-r . 156 i.' oo *11 6L -tt 1rt 6L ^ l- 11 - {l -r | {il1 bL ka AtvD Kl o -z,rsc I 3.\q1 -57. .{ 3.f.{.{ t t)S'od _3.t9rt ,37roo I o2.lsqoot 3.t,-{ t{ A 57. q -3"tq.{ | | 37 ?OO *3.t9 rt 7.?556OJ O 'l'lr5 A zo3q s -z(.1 z$3s ztz.oo -2D39 fo6aso l1r5 4 o -ZO3g 24,t -zo.3g to6ooo -2o3i ztzdc)q -1,16(l 1 lcta + -il.) ftta t l*troo. _llqt ttO.}sl r'\ lqf{l Ci I "It'.l? -.} tl.l -l{Ia t ?{. g,' {i llge ,&Z|DOJ FoA k,, ?q61 0 s7,Y 3Lt"l tl -216q 0 -57,\ 3llrl Lt rqtS 0 7A,I 2-o3g -1115 O '26.1 ro3g 5 o lrze K, b"= l.t 6r/ D o -l r{ 6'l c\ O a t\.7 l!qz $ 'll, I tlfl L il:' il- I !,=
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6, r{) {rar.rt,' G, . ?(r) - Fr, = 1! irr) If ,t) 6k I t r ^. .\\ t {.a,.' {-.1): i Fl, ,'*) ' F Fr r ,- - g-t'+ (rq) L i;,1',' " 3 \r lr - : * lLOt<iyr r /L \ FA, ll-'"q-.' -- $9.q5 ) a )s h ,.rla ;/a '' {' ( ce.' a l-- A= 67.9A" fx= ?S<os b $,'28.€5h {y= 75s'n O {} 6q.e3 k Ir FA, FA. O FS, +H'(zu) . 1,g!: ;^ F5, : lLth ,./r\3 FM, T# isi: = 3lt: 2'0 FFl,, lro xlv' F5. f. .. rva F,N4. FH. t-A {' (:) .^3' -T- _ (zq,sl) (. FAr Ftr FAr :6', F5,,' FS3=O FM1 = Ff{:=O :-ltl, tl3R hq FSr='3ti'6'* FM - = J'(:[il.' '13 - -LT_ . !*L t Ffir= r3 5D k;,^ i'i-r r{i:-}35th,'n r rt \? "vi? 1:ri)+is\\ - --L!- \{\aJ"Lt*'J f ='Y z :-fr{'q::k F$* {'l*j'((if 3/t )) ! ?" *31,62h , -L!l)'(:.l L. -Lf F r4u .,' l35O k i" i" fi) f 3Sox j"r l-< i FM" o \ vr,
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*lM 6.ri \ Ircnt,'. @' On Fl k s*,= ltlo h,* i c'k I t, I .''^t' i -lLo ri"j Qa.= - tI, r'!3 k sfl,6ek l3 5lk;" I,l.rl3 k 3'l ,6. zr. 1356k;^ Or (}h c hi" frk Op 0 kiq Qn: ' t*.".*'-* Qr, = 9.= b, g, t Q+, Memeeq I *tlF,.o : (rt€.rt)r (- tzd.fr) : n ,j"alaD CHEc,kg Qr = \.!. t Q{. Qr= \.9s * Qr, ?f, q6k ia, f"3 k 'ltrJKi-' ?c.q 6 k ab, ?3k ' lq tl3 hin rr--fFr.o (qq.toiol'h, €o) - -[-&nog ( " t|*,,'c (rt)(ra)(d\ {-59lJJ* i.:ti^j + (t{d(nklz) * i't)i' \ *o ^asj-1.1) r-*-"'*' I 1 -il .'l :1CI: l 'r(S li \/: bt lv\EmBER a "r/LFr.O = ( zr. 6S) + (ur ,Sg) * (- tq6,rq) =-.61 *$-fu4.'D (* Ll'\. =c *\lFr= O . ttq,aEi r f rr,or) + (-eo. rS) -,^'l *r.l zrn?b . (r'1,t3)+ (st%\- Uq.a:)jg$)lz)- rr,nt){trXra) 5,9 a" O _ &0oI Cue cns Q.= Iti.58k t!.alk t'1 il 3 k;\ FlA.rtrlk 80. r.5 k 5 tA0 r. i" ''l -t 1l l r.f. ;iv! i; l"j tt lio tf It I-l jil
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/ rr \ b, ir J {r,rni.} lqnt4e,.rntl t{Er4 gEc. 3 *\1r, - n = r*J.-. ., t n: * ll1"14) *-ljFy,a i * {y,_.n . {-li,i:'i,,'-trrli i_;r,a:)l.rl)1rar 6,qZ =Q 'G 6,D ) - A - / ta| , '\.' -/.urrk4 !rlu -r1i -- !'?*,;i:,) + ten,aj) ?, ! AAt, _ ) !'- f: {: l', [-t f, (i lCC '.'j ( i;:l'| 3 i". /' t' *:i n 6r ;1 r'1' l' r_i /i r, O,='\,ro Q." 1?Oo- {-?.36r' 6:= 11l" *'f,"",-' 1T.i'- d . llg, olo {= il t ;; I "I 1i f ,.*o i,v, & [-lire rosd J: I t: ln{: lr r Lf'f. 4.'1"r;.i?n o tfro ctl *l olrO 0CIf 0,t ol 0,3f,;rO lOl 0 Clf,''l o0i 0 **, o o rJ {r o o a I a.frnf :) \..) 'tJ iJ i \ fr C { ''.1c: -,3?S 0 | { ,1t5 -,'lal .ir I .' D !l r '- Q1-. '}ss l() It I I L-i I l.\ L ! n .., fq r', I I $ f-, t., +i CI '' Df r -.t;ii tg: 4 i -.{f: -,'lji D I {,: ii ,i, 1 j > l*: _ ?4( -,1? 3 |,. -.t?Tf .t*z -,Cta -.qTl ao o* F\I) 'L/ l;O
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4411_hw4_solutions - 'rtDf4E uoqk 6.11 I T !')+' t I I lU...

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