Math 166

Fall 2000

Final Exam

 

  1. (20 pt) Evaluate the following integrals:

a)            b)               c)                 d)

 

  1. (8 pt) Determine if the following sequences converge:

a)                 b)              

 

  1. (6pt) Suppose that you have a sequence  and you know that the sequence satisfies  for all

a)       What do we call such a sequence?

b)       If the sequence converges, what else must also be true?

  1. (8 pt) Suppose that you have an infinite series satisfying

a)       Find

b)       Find

  1. (20 pt) Determine if the following series converge:

a)                    b)         c)        d)

 

  1. (20 pt) Consider the functions and

a)       Find the area of the region bounded by and

b)       Find the centroid of the region from part a)

c)       Find the volume obtained when the region from a) is spun about the axis.

d)       Find the volume obtained when the region from a) is spun about the  axis.

 

  1. (8 pt) Consider the polar equation

a)       Sketch this polar curve.

b)       Find the total area enclosed by this curve.

  1. (6 pt) Find the interval of convergence of the power series
  2. (8 pt) Graph the parametric curve given by  

10.  (6 pt) Consider . Suppose that the graph of the 4th derivative of  is pictured below. How large should  be chosen so that the error of using is less than or equal to 1/20?

 

 

 

 

 

 


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