Math 165

Spring 2002

Exam 3

 

  1. (30 pt) Compute the following limits:

a)           b)           c)

 

d)              e)

 

  1. (15 pt) Sketch the graph of the function  For your convenience, the first two derivatives are:
  2. (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 ).

 

  1. (15 pt) Find the area of the largest rectangle that can be inscribed inside the ellipse  What happens if ? What should happen?

 

  1. (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.

 

  1. (10 pt) Consider the function

 

a)      Use logarithmic differentiation to compute

b)      Use part a) to show that  is constant. Find