Math 165
Spring 2002
Exam 3
- (30 pt) Compute the
following limits:
a) 
b) 
c) 
d) 
e) 
- (15 pt) Sketch the
graph of the function
For your
convenience, the first two derivatives are: 
- (20 pt) Sketch the
graph of the function
The first two
derivatives of the function are 
(Pay attention
to what the function looks like near 
).
- (15 pt) Find the area
of the largest rectangle that can be inscribed inside the ellipse
What happens if 
? What should happen?
- (20 pt) You wish to
construct a cylindrical storage can (with both a top and a bottom) of some
fixed volume. If you want to minimize the surface area of the can, show
that the height must be precisely twice the radius of the base.
- (10 pt) Consider the
function
a)
Use
logarithmic differentiation to compute 
b)
Use
part a) to show that 
is constant. Find 