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.