Math 166

Fall 2001

Final Exam

 

  1. (20 pt) Evaluate the following integrals:

a)    b)   c)       d)

  1. (20 pt) Consider the two curves  and

a)      Find the area between the two curves.

b)      Find the volume obtained when the region bounded by the curves is revolved about the axis.

c)      Find the length of the curve  (hint: 1 d) might be useful).

d)      Find the surface area obtained when  is revolved about the axis.

  1. (10 pt) Determine if the following sequences converge or diverge:

a)           b)  where each  is between 0 and 9.    

  1. (15 pt) Determine if each series converges or diverges:

a)     b)         c)

  1. (9 pt) Find the interval of convergence of the power series .
  2. (10 pt) Suppose that you want to use Simpson’s rule to evaluate . You find that the fourth derivative of your function is . How large should you choose  so that the error bound for Simpson’s Rule is less than or equal to
  3. (10 pt) Sketch the parametric curve  Indicate where the tangents are vertical and horizontal.
  4. (10 pt) Consider the polar equations  and

a)      Sketch both curves (indicating which is which).

b)      Find the area that is common to both curves (that is, the area inside both curves).

  1. (6 pt) Evaluate  with error less than or equal to

 

 

 

 

 

USEFUL STUFF: