APPM 2350 Final: appm2350summer2017examfinal_sol
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Summer 2017: (30 pts) consider the function g(x, y, z) = We want to determine the upward ux of the vector eld. 8 i + 4j + k through that portion of the level surface g(x, y, z) = 1 lying inside. 4 x2 + y2 = 1. g(x, y, z) = 1 = 4 y2 1 (c) find the integrand you will use to compute the requested ux. 2 x, y, 1(cid:29) upward ux so use g p = k = | g p| = 1 and f ( g) =(cid:28) . 2 y, 1(cid:29) = x+2y+1 (x + 2y + 1) da = zz. 4 y2 1 (x + 2y + 1) da (d) the region r is kind of messy when it comes to actually computing the ux so let"s consider the change of variables. Write an inequality describing the region in the uv-plane over which the integration will occur and v = u =
