Calculus Solutions 30

Calculus Solutions 30 - Answers t o Odd-Numbered Problems...

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Answers to Odd-Numbered Problems Sect ion 15.4 Surface Integrals (page 581) 2rr 2 1 N = -2xi - 2yj + k; dS = dl + 4x2 + 49 dx dy; lo /, d w r dr dB = :(17~/' - 1) 3~=-i+j+k;d~=fidxdy; area fir . -21- +k;dS= d2d 2~ 1/fi rdrd8 5N=d& 0 0 J--+fi) 7 N = -7j + = 5fi dx dy; area 5 4 ~ 9N=(y2-x2)i-2xyj+k;dS=~l+(y2- + 4x2y2dx dy = + (y2 + ~2)~dx dy; JtCJ,' dm r dr d0 = N = 2i + 2j + = 3dx dy; 3(area of triangle with 2% + 2y 5 = A= -sinu(cosv i+sinvj) +cosuk;B = -(3+cosu)sinvi+ (3+cosu)cosv j; N = -(3 + cosu)(cosucosv i +cosusinv j + sinu k);dS = (3 + cosu)du dv $J(-M~ - N% + P)dx dy = JJ(-2x2 - 23 + z)dx dy = -r2(r dr d0) = -87r F.N= -z+y+z=Oonplane N=-i-j+k,F=(v+u)i-uj,J~F.NdS=II-vdudv=~ JJ dS = so Jo + cos u)du dv = 127r2 31 Yes 33 No A = i+ f'cos0 j + f'sin0 k;B = -f sin8 j + f cos8 k;N = ff'i - f cos8 j - f sin0 k;dS = INldz dB = f (x)dm dx dB ldivF=l,JJJd~=Y 3divF=2~+2y+2z,~/$div~dV=0 5divF=3,~~3d~=~=~ 2~ ~/2 7 F N = pa, JJp=a p2dS = 47ra4 9 div F = 22, I. J: 2pcos 4(p2 sin 4 dp d# dB)
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This document was uploaded on 11/02/2011 for the course MAC 2311 at University of Florida.

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