HW3 Solutions

HW3 Solutions - 2-1=1 ~ V-l R = l l'x~ ~"2 ~ sh ~ ~2 4)lh...

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2.-1=1 ~) V(-l) = \] (l ) R. \: l'x~+~ "2+~?) sh. = J.. (--L \ Q~ + -l. f---L \~ +2 ( --l . \Q-c dX ~'+~2+4)lh) o~ ,&1-+~"1+i-YJl-) dt \('t(~"Z.+~1..)I/2.-) -?>/-z... _ l."l -3/2.. _ -3/'"2.. ~ --L l -X-L+Ul. -t -l"L) l2.X'jo...x -J.l~ + ~ t "2;~) l~ )a.~ - .ll~'"L+lJL ttL) (21.;) o-'t ~ u ~ ~ ~ -~/~ ~ - (y.1.. +~"2. + 1::') L lC O-.y. -t ~ O-..~ +- 1- 0...2:. ") by v( i):: 2 C i) CL,c +.-L2J t) lr e -t (~ c-lJ ~~) ~ oR. R~ ~ ~~Ine- o 0 Q} Qoy = loS t ~x + SIY\ ¢ QJ a.~ z: - cs.'IY\ ~ 0...)( + Uj;. ~ a: ~ dQ:o.= .2 llO~~ ~Y- + SlY( ~ ~ ") _ "" <p d cP -a. '(' CA y- :: - 'S\ Y1 ~ Q..y. + wS:. d Q j I := - si~ cP ( CD~4 ety --siYl ¢ o..~ ') + los~ (s(Y) cP cfr- + 0.4 ') ~ Q4> ~ = 2 L-S;Y\~ Cl-~ + ~~ Q'j ') () c\> 'd4 -= - Co~ ~ 0.. y. - s\ Yl d a. ~ -=- - ( D £..~ (c.a;.d a)" - ~; Yl ~ a lil ') - S I' V1 4( os \ n ~ a'6 t- CD s,. cb Q ~ ) = - 0."(
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b) \l:: 0."'( k +- C\.~-.2 + Cl.~ l dY YO~ dt A = A-y ()y + A q o..<i + A:c. Gt:e. A::.. 0.."(. [0-. 'Y .2 «; + 0.4> "6 A f + 2i"to d At] -----') dAn 0"( ~ 07::. , )y + etJ, [J...Q (A~y + A-~ GC¢ + A~Cl-"b >J - 'I' "Y a~ - - lty a~ ~ S ~ CAlf>' [J .1 Ay- Q,y + li-.'r ~ -t .L ~A~ ct~ -r M ~~ t Y dQ; y d~ '"'0 ""d¢ Ir <7¢ +-l~I+-~~ + ~ ~] 1 r d <:b "Y "";J ep ~ + Q1. . l 0'0 it ().. y -t ~ ~ A ~ + Cl~ ~ A ~J 0 d~ d~ de - V . A =' d t\"'r -+ ~ ~ +- &r + ~ A-=l:. 0"0 ')- de? y "d:r. e, _\ ~ ( ,I\y) + --l * --t d A-=t::. r d",( Y dep d~ ) .. - 2.l Q) ---- .. J \ .: ' ./ . I I I I .' 1~' _ ..- •• ~ Ii " " ~ ~ j 1 F 1;~"1l-0j ') + 11 r= ! .~(h (tX:,,) -x.- -- - - i _.'/ + 1 {F.
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