APPM 2350 Midterm: appm2350spring2016exam3
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Instructions: books, notes, crib sheets, and electronic devices are not permitted. Write your (1) name, (2) instructor"s name, (3) recitation number. To impress his parents, rusty drills a hole straight down through a sphere. (if you"ve ever tried it, you know it is not an easy task. ) The hole is described by r = 2 cos , and the solid sphere is described by x2 + y2 + z2. Nd the area, a, of the enclosed region. The substitutions u = 3x + y and v = y + 4 will simplify your calculation. (a) solve for x and y in terms of u and v using the given substitutions. Be sure to check this because the rest of the problem depends on these results! (b) transform the original region rxy into its corresponding region ruv in the u-v plane. Make a clear sketch of the new region of integration ruv in the u-v plane.
