1. (20 pt) Compute the following limits:

a) b) c)

d) e)

2. (10 pt)Use the definition of the derivative to compute the derivative of

3. (20pt) Compute the derivatives of the following functions (use any method that you like).

a) b)

c) d)

4. (16 pt) I shoot a cannonball straight up in the air so that its position is given by .

a) When does the cannonball return to the ground?

b) Find an equation for the velocity of the cannonball at any time t.

c) How fast did I shoot the cannonball?

d) How high does the cannonball go?

5. (10 pt) Find all asymptotes (horizontal and vertical) of the function

6. (6 pt) Let and . Find

7. (12 pt) Answer the following questions for the function pictured below:

a) Where is f(x) continuous?

b) Where is f(x) differentiable?

c) Sketch f¢ (x).

8. (6 pt) Show that the function has a root.