Let F (x, y, z) = x2yi + 2xzj + (z3 + 4x2)k andlet Sa be the sphere of radius a centered
Chapter 20, Problem 52(choose chapter or problem)
Let F (x, y, z) = x2yi + 2xzj + (z3 + 4x2)k andlet Sa be the sphere of radius a centered at (1, 1, 1),oriented outward, parameterized by r (, ) = (1 +a sin cos )i + (1 + a sin sin )j + (1 + a cos )k ,0 , 0 2.(a) Compute div F (1, 1, 1) .(b) Use the geometric definition of divergence to estimateSa F dA for a = 0.1.(c) Evaluate the flux integralSa F dA . Compare itsvalue for a = 0.1 with your answer to part (b). Thencompute the limitlima0Sa F dAVolume inside Saand compare your result with part (a). Explain youranswer in terms of the geometric definition of thedivergence.
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