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Calculus Solutions 31

Calculus Solutions 31 - A-30 Answers to Odd-Numbered...

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A-30 Answers to Odd-Numbered Problems 15 Both integrals equal F dR; Divergence Theorem, V = region between S and T, always div curl F = 0 17 Always div curl F = 0 19 f = xz + y 21 f = e2-' 23 F = yk 25 curl F = (ask - a2bs)i + (alb3 - a3bl)j + (a2bl - alba)k 27 curl F = 2wk; curl F . = 2w/4 29 F = x(a3z + a2y)i + y(alx + a3z)j + z(alx + a2y)k 2% r/2 31 F = -2k, JJ -2k . RdS = Jo -2 cos 4(sin 4 d4 dB) = -2r; J y dx - x dy = J:"(- sin2 t - cos2 t)dt = -2r 2% %/2 33 F = 2a, 2 //(alx + a2y + a3z)dS = 0 + 0 + 2a3 Jo cos 4 sin 4 d4 dB = 35 F = -i,n = *,JIB' .ndS = -~rr~ h A 37p=d-I'= stream function; zero divergence 39 div F = div (V + W) = div V so y = div V so V = \$j (has zero curl). Then W
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