2004 Fall - 125FinalFall04short math125

2004 Fall - 125FinalFall04short math125 - MATH 125 FINAL...

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MATH 125 FINAL EXAM (common exam) December 2004 1. (5 points each) Compute the following limits, if they exist. You may not use l’Hˆopital’s rule, if you know what that is. You must also justify your answer. (a) lim x + 3 x 2 + 1 (1 - x )(2 x - 1) (b) lim x 0 x cot 7 x (c) lim x 1 5 - x - 4 x x 2 - 1 2. (6 points each) Find dy dx of the following functions. (You do not need to simplify your answer.) (a) y = sin ( ln(1 + x 100 ) ) (b) y = x e e x (c) y = Z x 0 (1 + e - t 2 ) dt (d) y = tan x 1 + sec x 3. (6 points each) Evaluate the following integrals. (You do not need to simplify your answer.) (a) Z ± 5 x 2 + 1 x + 2 cos 2 x - sin x ² dx (b) Z 1 0 x cos(1 + x 2 ) dx (c) Z 5 x 1 + 5 x dx 4. (12 points) Knowing that 4 81 = 3, use a linear approximation to estimate 4 85. 5. (15 points) Find an equation of the tangent line to the curve xe 2 x - y 2 ln y = 0 at the point (1 , e ).
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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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2004 Fall - 125FinalFall04short math125 - MATH 125 FINAL...

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