2005 Fall (short) - 125FinalFall05shrt math125

2005 Fall (short) - 125FinalFall05shrt math125 - MATH 125,...

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Unformatted text preview: MATH 125, FINAL EXAM (common) December 2005 1. (6 points each) Calculate the following limits. a) lim x 4 x- 4 x- 2 . b) lim x 1 e x- e x- 1 . c) lim x 3 x + x 2 sin x . 2. (7 points each) Find dy dx . a) y = ln(2 x 2- 3 x ). b) y = 2 x- 3 e x +1 . c) y = x sin x (Use logarithmic differentiation). d) y = Z tan x t 2 + 4 dt for- 2 x 2 . 3. (8 points each) Evaluate the following integrals: (a) Z 2 1 x 2 ( x- 2) 2 5 dx . (b) Z sin x x dx . (c) Find the area of the region bounded by the curves y = 0, y = xe x 2 , x = 0 and x = 1. 4. Consider the following function and its first and second derivative: f ( x ) = x x 2 + 4 f ( x ) =- x 2- 4 ( x 2 + 4) 2 f ( x ) = 2 x ( x 2- 12) ( x 2 + 4) 3 . a) (5 points) Find the critical numbers of f . b) (10 points) Determine where f is increasing, where f is decreasing, and find the local maxima and minima of f . c) (5 points) Find the asymptotes of f ....
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This note was uploaded on 09/03/2008 for the course MATH 125 taught by Professor Tuffaha during the Fall '07 term at USC.

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2005 Fall (short) - 125FinalFall05shrt math125 - MATH 125,...

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