1. (25 pt) Compute the following limits:

a) b) c)

d) e)

 

2. (7 pt) Use the definition of the derivative to find if .
3. (25 pt) Compute the derivatives of the following functions

 

a) b) c)

d) e)

 

4. (8 pt) Find the tangent line to the curve at the point (-1,2).
5. (20 pt) A cannonball is fired up in the air from the top of a building so that its height (in feet) above the ground at any time t (in seconds) is given by

1. How tall is the building?
2. When does the cannonball hit the ground?
3. Find an equation that gives the velocity of the cannonball at any time.
4. How high does the cannonball go?

1. (15 pt) Use the graph below to answer the following questions:

1. Copy the graph and tell where you think the function is continuous (explain).
2. Where you think the function is differentiable (explain).

c) Find all points where the limit of the function does not exist and explain (tell whether the left and/or right limits exist at these points also).