1. (20 pt) Find the following limits:

a) b) c)

d) e)

2. (20 pt) Find the most general antiderivatives for the following functions:

a) b) c)

d) e)

3. (10 pt) Find the area under , for . Use the definition of the definite integral.

4. (5 pt) Use the fundamental theorem of calculus to check your answer in #3.

5. (5 pt) Find . (Hint: What does the function look like?)

6. (10 pt) Use the fundamental theorem of calculus to show that and . (Hint: cos(-x)=cos(x) and sin(-x)=-sin(x)).

7. (15 pt) Evaluate the following:

a) b) () c)

8. (15 pt) Consider the function .

a) Find all critical points of the function.

b) Find the absolute max and min values of the function on the interval [-2,4].