1. (20 pt) Evaluate the following limits.

a) b)

c) d)

e)

2. (15 pt) Use the definition of the derivative to find the tangent line to y=2x²/(x+1) at the point (1,1).

3. (20 pt) Compute the derivatives of the following functions.

a) b)

c) d)

4. (5 pt) Consider the function , find or show that it does not exist. Use this information to sketch the graph of .

5. (15 pt) Consider the following graph of a function.

Where is f(x) continuous? Sketch the graph of the derivative of f(x) (be sure to indicate where the derivative does not exist).

6. (5 pt) Let f(x) be a function such that 1<f(x)<3 for all -1<x<1. Compute the limit as x goes to zero of x²f(x)+2.

7. (5 pt) Let f(x) be a continuous function such that f(2)=3. Compute . Justify your answer.

8. (15 pt) I throw a ball up in the air so that its height above the ground at any time t is given by s(t)=64t-16t².

a) When does the ball hit the ground?

b) When is the velocity of the ball 0?

c) What is the ball’s height at this moment?