MATH 161

EXAM 3

 

  1. (15 pt) Sketch the graph of the parametric equation , . Find the tangent line at .

  2. (15 pt) Find the area enclosed by and the length of the polar equation , sketch the curve.

    3.  

  3. (10 pt) Determine if the following sequences converge.

 

a) b) where is the partial sum of the harmonic series (i.e. ).

 

4. (25 pt) Determine if the following series converge make clear the test that you are using:

 

a) b) c)

 

d) e)

 

  1. (10 pt) Determine if the following two series converge. If they do, then find the sum.

    2.  

    a) b) where the partial sum is given by.

     

  2. (10 pt) The following two series converge, how many terms should we add up so that the error is less than .001?

    3.  

    a) b)

     

  3. (15 pt) Find the center, radius and interval of convergence of the following power series:

    4.  

     

  4. (10 pt) Extra credit: Determine of the following sequence converges. If it does find the limit:

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