Math 222 – Practice Exam 1 w Solutions 2011 – Calculus 2

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Math 222 Calculus 2 Fall 2008 Exam 1(1) (10 Points) Let the differentiable function y = f(x) have inverse function x = f −1 (y).(a) Write down the formula relating the derivatives f ′ (x) and (f −1 ) ′ (y). (No workneeds to be shown.)(b) For the specific function f(x) = x 5 + x 3 + x explain why f(x) has an inversefunction.(c) For y = f(x) = x 5 + x 3 + x, use your answer to part (a) to find (f −1 ) ′ (3). Notethat f(1) = 3.(2) (10 Points) Simplify each of the following expressions.(a) cos −1 ( √ 3/2).(b) ln(5 x√x )
(3) (5 Points) Use the fact that limx→∞Math 222 Calculus 2 Fall 2008 Exam 1(1 +x) 1 x= e to find limn→∞(1 + 23n) n.(4) (15 Points) Find each of these derivatives.(a)ddx sin−1 (x 3 )(b)ddx 3tan−1 (x)(c)ddx log 2(x 4 + x 2 + 1)
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Math 222 – Practice Exam 1 w Solutions 2011 – Calculus 2

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