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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 + 4 9 dx dy; lo /, d w r dr dB = :(17~/' - 1) 3 ~ = - i + j + k ; d ~ = f i d x d y ; area fir . -21- + k ; d S = d2d 2~ 1 / f i rdrd8 5 N = d & 0 0 J--+fi) 7 N = -7j + k; dS = 5 f i dx dy; area 5 4 ~ 9 N = ( y 2 - x 2 ) i - 2 x y j + k ; d S = ~ l + ( y 2 - + 4x2y2dx dy = dl + (y2 + ~ 2 ) ~ d x dy; JtCJ,' d m r dr d0 = N = 2i + 2j + k; dS = 3dx dy; 3(area of triangle with 2% + 2y 5 1) = 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 - 2 3 + z)dx dy = -r2(r dr d0) = -87r F . N = -z+y+z=Oonplane N = - i - j + k , F = ( v + u ) i - u j , J ~ F . N d S = I I - v d u d v = ~ 2rr 2rr JJ dS = so Jo (3 + 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 ) d m dx dB l d i v F = l , J J J d ~ = Y 3 d i v F = 2 ~ + 2 y + 2 z , ~ / \$ d i v ~ d V = 0 5 d i v F = 3 , ~ ~ 3 d ~ = ~ = ~ 2~ ~ / 2 7 F N = pa, JJp=a p2dS = 47ra4 9 div F = 22, lo I. J : 2pcos 4(p2 sin
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