MATH10550 Final: MATH 10550 Final Exam Spring 2012
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25. (d) (d) (d) (d) (d) (d) (b) (b) (b) (b) (a) (a) (a) (a) (c) (c) (c) (c) (c) (c) (e) (e) (e) (e) (e) (e) (d) (b) (a) (c) (e) Let f (x) = ex 1 and let f 1 denote the inverse function. Then (f 1) (e2 1) = is (a) e 1 (d) e2 (b) (e) Solve the following equation for x: ln(x + 4) ln x = 1 . x = and x = 4 e 1 e + 1 x = e + 2 and x = e 2 (a) x = 1 e (c) there is no solution. (e) x = Find the derivative of (x2 + 1)x2+1. (a) (b) (c) (d) (x2 + 1)x2+1(cid:0)2x ln(x2 + 1)(cid:1) (x2 + 1)x2+1 2x(cid:0)ln(x2 + 1) + 1(cid:1) 2x(x2 + 1)x2 (x2 + 1)x2+1 (e) this function is not de ned and hence has no derivative.
