15. (4 pts) Use L’Hôpital’s Rule to find each limit. a)

4. (4 pts) Let

3. (6 pts) Evaluate each limit. Do not use L’Hopital’s rule on these problems. a)

12. (8 pts) Let

7. (4 pts) Given this equation, find dy/dx:

6. (8 pts) Find the derivative of each function. a)

11. (5 pts) Let

8. (6 pts) Sand is being dumped from a conveyor belt at a rate of 35 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 6 feet high? Round your answer to four decimal places. Note that the volume of a cone is given by V = (1/3) πr2h where r is the radius of the base of the cone and h is the height of the cone.

4. (4 pts) Let  

For questions 1 and 2, refer to the graph of y = f(x) shown below.     1. (6 pts) For each value of a, find: the limit of f(x) as x approaches a from the left the limit of f(x) as x approaches a from the right the limit of f(x) as x approaches a f(a) a) a = -4 b) a = 2 c) a = 4     2. (4 pts) Use the same graph as in #1. Find the three x-values at which f(x) is discontinuous. For each one: a) Using concepts of limits, explain (briefly – a few words) why the function is discontinuous at this value. b) Classify the discontinuity as removable, jump, or infinite. You do not have to explain.