2002 Spring - Spring_2002 math125

# 2002 Spring - Spring_2002 math125 - Math 125 Spring 2002...

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Math 125, Spring 2002, Calculus I FINAL EXAM Problem 1. Evaluate the following limits (finite or infinite). Use only the techniques seen in this course. In particular, you are not allowed to use L’Hospital’s rule if you know what this is. a. (8 points) lim x 4 + r 4 x x - 4 b. (8 points) lim x 0 + ln x 4 + 3 ln x Problem 2. Evaluate the following limits (finite or infinite). Use only the techniques seen in this course. In particular, you are not allowed to use L’Hospital’s rule if you know what this is. a. (8 points) lim x →∞ ( p e 2 x + e x - e x ) b. (8 points) lim x e ln x - 1 x - e (Possible hint: Could this be a derivative?) Problem 3. Differentiate the following functions: a. (8 points) f ( x ) = ln(1 + x x ) b. (8 points) g ( x ) = ( x 2 + 1) 5 e x + 1(5 sin( x ) + 1) 2 (Suggestion: logarithmic differentiation, by computing the derivative of the natural log of the function) Problem 4. (8 points) Differentiate the following function and simplify your answer: h ( x ) = Z ln x x e t 2 dt Problem 5. (8 points) Evaluate the following integral: Z 2 0 | 1 - x 2 | dx Problem 6.

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