APPM 1360 Final: appm1360summer2013examfinal_sol1
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2. (b) (4 pts) write out the full partial fraction decomposition of coe cients. 0 xe xdx integrate by parts with u = x, du = dx, v = 1. E t x4 + 3x3 + 2x2 = E x, dv = e xdx to get: t. Summer 2013 (a) (6 pts) find the x-coordinate of the center of mass of the in nite region bounded by x = 0, y = 0 and y = e x, where > 0. You may use the fact that z . Do not determine the (a) (4 pts) suppose the nth partial sum of the series p an is given by sn = n1/n. Find an expression for the nth term of the series, an. Do not simplify your answer. (b) (4 pts) determine whether the series above is convergent or divergent. (c) (6 pts) is the series sin n (n2 + cos2 n) arctan n absolutely convergent, conditionally convergent or diver-
