Math 160
Fall 1999
Final Exam
1. (20 pt) Find the following limits:
a) 
b) 
c) 
d) 
e) 
2. (20 pt) Find the derivatives of the following functions you may assume that the derivative(s) of any unknown functions exist:
a) 
b) 
c) 
d) 
3. (20 pt) Evaluate the following integrals:
a) 
b) 
c) 
d) 
4.
(10 pt) Use the definition of the derivative to find the
derivative of 
. Check your answer.
5.
(10 pt) Use the definition of the definite integral to
evaluate 
Check your answer.
6.
(5 pt) Find the tangent line to the curve 
at the point 
7.
(10 pt) Sketch the curve 
. Show your work.
8.
(10 pt) Find the point on the line 
that is closest to
the origin.
9.
(5 pt) Find the area that lies under the curve 
(
) between 
and 
What happens to your
answer as 