Math 166

Fall 2001

Exam 3

1. (15 pt) Determine whether the following sequences converge:

a)               b)  where  is the  partial sum of the positive term series                             c)

1. (36 pt) Determine if the following series converge:

a)         b) c)                d)

e)      f)

1. (10 pt) Both series  and  converge.

a)       Find the smallest so that the error of estimating  with the  partial sum gives an error bound less than or equal to .01.

b)       Find the smallest so that the error of estimating  with the  partial sum gives an error bound less than or equal to .01.

1. (16 pt) Find the center, radius, and interval of convergence of the power series

1. (18 pt) Consider the function

a)       Find a series for  centered at  What is its radius of convergence?

b)       Use your series to show that

c)       How many terms are necessary so that using the  partial sum of the series above to estimate gives an error bound of less than .01?

1. (15 pt) Consider the functions  and

a)       Find Maclaurin series for and

b)       Evaluate with error less than or equal to

c)      Evaluate