Math 165
Fall 2002
Final Exam
- (24 pt) Find
derivatives for the following functions:
a) 
b)
c) 
d)
- (20 pt) Find the
following limits:
a) 
b) 
c) 
d) 
- (24 pt) Evaluate the
following integrals:
a) 
b) 
c) 
d) 
- (5 pt) Use the definition
of the definite integral to find
with 
a constant. - (5 pt) Use the
definition of the derivative to find the derivative of
- (8 pt) Find the volume
of the maximal (with respect to volume) cylinder that can be inscribed in
a sphere of radius
- (5 pt) Use a linear
approximation to estimate
. - (5 pt) Suppose that you
wish to use Newton’s Method to estimate the smallest positive root of
You discover
that this root occurs between 0 and 1. Which (of the numbers 0 or 1)
should you choose as an initial approximation for Newton’s Method (Do they
both work? Why or why not?). - (8 pt) Sketch the graph
of the function
You may assume
that this function has the 
axis as a vertical asymptote. - (6 pt) Suppose that a
spherical balloon is deflating so that its radius is decreasing at 1 inch
every 2 seconds. How fast is the surface area of the balloon changing when
the balloon’s radius is 2 inches?