Math 165
Spring 2002
Exam 3
- (30 pt) Compute the
following limits:
a)
b)
c) ![](./M165.3.S2002_files/image006.gif)
d)
e) ![](./M165.3.S2002_files/image010.gif)
- (15 pt) Sketch the
graph of the function
For your
convenience, the first two derivatives are: ![](./M165.3.S2002_files/image014.gif)
- (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
![](./M165.3.S2002_files/image026.gif)
a)
Use
logarithmic differentiation to compute ![](./M165.3.S2002_files/image028.gif)
b)
Use
part a) to show that
is constant. Find ![](./M165.3.S2002_files/image032.gif)