MATH 180 Study Guide - Final Guide: Quotient Rule, Product Rule, Asymptote
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Problem 1 solution: di erentiate with respect to x. Write your answers showing the use of the appropriate techniques. Do not simplify. (a) (x2 + 1) sin(x) (b) 5x 3 x2 + x + 1 (c) ex. [(x2 + 1) sin(x)] = (x2 + 1)(sin(x)) + (x2 + 1) sin(x) = (x2 + 1) cos x + 2x sin x (b) use the quotient rule. x2 + x + 1(cid:19) (cid:18) 5x 3 (x2 + x + 1)(5x 3) . (5x 3)(x2 + x + 1) (x2 + x + 1)2 (x2 + x + 1)(5) (5x 3)(2x + 1) (x2 + x + 1)2 (c) use the chain rule. (ex. Solution: (a) the area of the region is given by the integral: 0 (4x x3) dx (b) we use ftc i to evaluate the integral. Solution: upon substituting x = 0 into the function we nd that. We resolve this indeterminacy by using l"h opital"s rule. lim x 0.
