2001 Fall - Fall_2001 math125

# 2001 Fall - Fall_2001 math125 - Math 125 Spring 2002...

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Math 125, Spring 2002, Calculus I PRACTICE FINAL EXAM (This was the final exam for Math 125 in the Fall 2001 semester) Instructions: Try all the problems and show all your work. Answers given with no indica- tion of how they were obtained may receive no credit. If you need more space, write on the back of another page and clearly mark on your problem that it is continued elsewhere. Problem 1. (45 points) Find the limits. a. lim x 4 x 2 - 5 x + 4 x - 4 b. lim x →-∞ x 2 + 1 2 x - 5 c. lim x 0 sin 3 x x + sin 4 x Problem 2. (15 points) Find a constant c for which the following function f is continuous on ( -∞ , ). f ( x ) = ( 2 x 2 + cx if x 1 x 2 - 2 x - c if x < 1 Problem 3. (30 points) Find dy/dx if a. y = e x sin x b. y = ln(sec x + tan x ). Simplify the result. Problem 4. (60 points) Consider the function f ( x ) = 3 x 5 - 5 x 3 . Sketch a graph of the function f , and indicate on the dotted lines below: (1) the intervals where the function is increasing (if any): . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2) the intervals where the function is decreasing (if any): . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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