Math 165

Spring 2001

Final Exam

 

  1. (20 pt) Compute the following limits:

a)          b)              c)               d)       

 

  1. (20 pt) Find the derivatives of the following functions:

a)               b)         c)

 

d)

 

  1. (25 pt) Find the following integrals:

a)            b)           c)

 

d)            e)

 

 

  1. (10 pt) A spherical bubble’s volume is increasing at 10 cm3/s. Find the rate of change of its surface area when the radius of the sphere is 20 cm.

 

  1. (10 pt) Show that among all rectangles with fixed area A, a square has the smallest perimeter.
  2. (10 pt) Sketch the curve

 

  1. (5 pt) Use the definition of the derivative to find the derivative of Check your answer. 

 

  1. (5 pt) Find the tangent line to the curve  at the point

 

  1. (5 pt) Suppose that you are using Newton’s Method to find a root of Suppose is continuous and has two derivatives everywhere. Also suppose that there is an interval containing the root where the function is both increasing and concave down. If Newton’s Method converges to this root, will the approximations be too big, too small, random, or is there not enough information to tell? Explain.