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6. [8+7=15 Points] For r> 0, let S, denote the sphere of radius r with center at the origin, oriented with outward normal. Suppose

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6. [8+7=15 Points] For r> 0, let S, denote the sphere of radius r with center at the origin, oriented with outward normal. Suppose F: R3 R is of class C and is such that for fixed constants a and b. (a) Compute F dS ar+b S V.FdV, where D ((x, y, z) e R 125 0. What conditions does this place on the constants a and b?

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