Sample Midterm Exam 2

Question 1 (10).
Find the derivative of the following functions:

a.

b.

c.

d.

e.

Question 2 (15). a. State the definition of the derivative of a function at a point .

b. Use the definition of the derivative to compute for

Question 3 (10). Find all the vertical and horizontal asymptotes of the graph of

Question 4 (20). For each of the following, either find the limit or state that "no limit exists" and briefly explain why. Show work used to get your answer.

a.

b.

c.

d. .

Question 5 (10). For the function

a. Find the equation of the tangent line to the graph of at the point (0,-2).

b. Show that at some point.

Question 6 (10)
a. State the precise definition of what is meant by
.

Use the precise definition of the limit to prove that .

Question 7 (5) Give an example of a function which is continuous at but not differentiable at .

Question 8 (5) Suppose and are functions and Where can you calculate the derivative of ? What is it equal to?

Question 9 (5) Let . Find .

Question 10 (10).
Find an anti-derivative of the following functions:

a.

b.

c.