1. (15 pt) Evaluate the following limits:

a) b) c)

2. (15 pt) Find the derivatives of the following functions:

a) b) c)

3. (7 pt) Use the definition of the derivative to find the derivative of .

4. (7 pt) Use the definition of the definite integral to find .

5. (15 pt) Evaluate the following

a) b) c)

6. (15 pt) Consider the graph of the following function :

a) Where is f(x) continuous and where is f(x) differentiable?

b) Sketch f¢ (x).

c) Sketch an antiderivative of f(x).

7. (10 pt) Sketch the graph of . For your convenience, the first two derivatives of this are and .

8. (10 pt) Two cars take off at the same time from the same point. One car goes east at 60 miles per hour and the other goes south at 30 miles per hour. How fast is the distance between them changing two hours later?

9. (6 pt) Find the tangent line to the graph of at the point (1,4).

10. (EXTRA CREDIT: 10 pt) A box is to be constructed with a bottom, four sides and no top. The width of one of the sides of the bottom is to be twice the width of the other side. If there is 36 square feet of material to be used, how do you construct the box to maximize the volume?