1. (25 pt) Evaluate the following limits:

a) b) c)

d) e)

2. (6 pt) Find the following limit:

Hint: rewrite this as a definite integral.

3. (10 pt) Use the definition of the definite integral to evaluate .

4. (6 pt) Consider the function , where if and if . Find the function . Is it true that ?

5. (6 pt) Find the derivative of .

6. (15 pt) Evaluate the following:

a) b) c)

7. (15 pt) Consider the function .

a) Find all local extrema of the function.

b) Use this information to sketch the graph.

c) Find the absolute maximum and minimum values on [-1,4].

8. (10 pt) You are on a planet with constant gravity (acceleration) g. You throw a ball up at initial velocity v₀. Find the position function of the ball (assume that the initial position is 0).

9. (7 pt) Consider the graph of . Given that the antiderivative F(x) satisfies F(0)=0, sketch the graph of F(x).