MATH 161

EXAM 3

 

  1. (20 pt) Determine if the following sequences converge or diverge.

    2.  

    a) b) where

     

    c) d)

     

  2. (30 pt) Determine if the following series converge or diverge.

    3.  

    a) b) c)

     

    d) e) f)

     

  3. (12 pt) Consider a series with partial sums given by the formula
.
  1. Find the sum of the series or explain why there is not enough information given.
  2. Compute
or explain why there is not enough information given.

 

  1. (12 pt) Find all values of for which the series converges.
  2. (12 pt) Consider the polar equation
.
  1. Graph the polar equation.
  2. Find the area of the inner loop.

 

  1. (12 pt) Consider the parametric curve given by the equations
.
  1. Find the length from the point (1,-3) to (2,-1).
  2. Find the tangent line to this curve at the point (2,-1).

 

  1. (12 pt) a) How many terms do we need so that estimating the series by the
th partial sum has error less than .001.

b) How many terms do we need so that estimating the series by the th partial sum has error less than .001.