To receive full credit you must show all work. You are allowed to use an approved graphing calculator unless otherwise indicated. There are 15 problems worth a total of 200 points. 2 hours: (10 points) use the de nition of the derivative to di erentiate the following function. f (x) = 1 x2 + 1: (7 points each) find the exact value of each of the following limits. , , or does not exist if appropriate. It is particularly important to show your work on this problem. (a) lim x 2 (b) lim x x2 3x + 2 x2 x 2 x2e x (c) lim x arctan(x) + x2. 1: (10 points) the graph of a function f is shown below. Sketch the graph of f : (12 points) at 1:59 pm a car leaves an intersection heading east at a constant rate of 40 ft/sec.
