APPM 1350 Midterm: appm1350fall2016exam3_sol
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Fall 2016: (21 pts) evaluate each of the following. (a) z sec2(1/x2) x3 dx (b) z 2. Solution: (a) (7 pts) let u = 1/x2, du = 2/x3 dx. Z sec2(1/x2) dx = z x3 sec2 u du = . 2 tan(1/x2) + c (b) (7 pts) let u = 1 + 2t2, du = 4t dt. 1 + 2t2 dt = (c) (7 pts) let u = 2t + 1, du = 2 dt. 5 du u: (15 pts) let f (x) = x4 and b > 0 be constant. 2 (cid:0)ln(cid:12)(cid:12)2x2 + 1(cid:12)(cid:12) ln 5(cid:1) = 5 (cid:12)(cid:12)(cid:12)(cid:12) (a) find the average value of f (x) on the interval [0, b]. (b) using your answer to part (a), nd the appropriate value of c from the mean value theorem for. Integrals. (c) find the value of lim n n.
