TURN OFF CELL PHONES,
BEEPERS, AND CHIMING WATCHES.
KEEP YOUR EYES ON
YOUR OWN PAPER.
INSTRUCTIONS FOR PART I: Write your answers for these questions on a scantron (form 882-ES or 882-E) and mark only one answer per question. On the scantron form, print your name legibly and indicate the final exam version (either A or B).
Each of the questions in this part counts 5 points each, for a total possible score of 45
points. You may use a calculator. You may write on this exam or request scratch
paper if needed.
1. Find the difference quotient for 
and 
A. 
B. 
C. 
D. 
E. 
2. Find an equation of the line tangent to 
at the point (1,3).
A. 
B. 
C. 
D. 
E. 
3. If 
, then find
A. does not exist B.
2 C. 1 D. 0 E. 
4. If 
, find 
A. 
B. 
C. 
D. A. 
E. 
5. Which of the following functions is continuous at the point (1,0) but not differentiable at (1,0)?
A. 
B. 
C. 
D. 
E. no such function exists
6. Find 
if 
A. 1 B.
C. 0 D.
not enough information given
E. does not exist
7. Determine c so that the following function is continuous. Choose an interval that contains c.
A.. 
B. 
C. 
D. 
E. 
8. Suppose 
Compute 
A. 1 B. 
C. 0 D. 
E. 
9. If f and g are differentiable functions such that
and 
find 
A. 0 B. 5 C. 4 D.
E. not enough
information given
10. If f and g are differentiable functions such that
and 
find 
A. 
B. 
C. 
D. 0 E. not enough information given
11. Find 
A. 
B. 
C. 
D. does not
exist E. 0
12. If 
what is 
?
A. 9 B. 2 C. 106 D. 25 E. 0
13. Solve for x: 
A. 4 B.
C. no
solutions D. 
E. 
14. If f and g are continuous functions with 
and 
find 
A.0 B. 6 C. 3 E. 5 E. not enough information given
15. Find an equation of the normal line to the graph of at 
.
A. 
B. 
C. 
D. 
E. 
INSTRUCTIONS FOR PART II: For these questions, you should write down all steps in your solutions. Write legibly and carefully label any graphs or pictures. Partial credit will be given for those parts of your solution that are correct. Each of the questions in this part counts 11 points, for a total possible score of 55 points.
16. Find the point(s) on the graph of 
where the tangent line
to the graph of 
is parallel to the
line 
17. Use the definition of the derivative to show that 
when 
18. Use the quotient rule to determine the derivative of 
19. Find an equation for the tangent line to the graph of 
at the point with x-coordinate 1.
20. Evaluate 
without using a calculator
or L’Hôpital’s rule.