Calculus 2  Hour Exam 3  (continued)   -   Math 231     Spring, 2012

 

 

 

 

4.

 

 

                    ∞

Let    f(x)  = ∑   x2n / n2                          Find:  f(10) (0)

                   n=1

 

a.       0               b.  1/100            c.  1/25          d.  10! / 100            e.  10! / 25

 

Answer:  a.

 

 

 

 

 

 

 

5.

 

Indicate   TRUE  or   FALSE  for each of the following statements.

                                                                              

a.       If the Maclaurin series for  f(x) = Σ cnxn has a radius of convergence  R,

                                                                                        x

then so do the Maclaurin series for  f '(x) and for  ∫ f(t) dt

                                                                                             0

                                                    ∞

b.      Suppose a power series   Σ an(x – c)n  has a radius of convergence  R.

                                       n=0

            Whenever     c – R  <  x  <  c + R , the series is conditionally convergent.

 

Answers:   a.   True         b.  False

 

 

 

 

6.

 

 

Find the radius of convergence of the series

                          

            ∞                                              

∑   n2 ( x + 1)3n + 2  / 8n               Answer:  R = 2     

           n=1                                                       

 

 

 

 

7.

 

 

Find the interval of convergence of the series

 

            ∞                                             

∑   [1 / (n + 1) 3n ] ( x - 2)n + 1                Answer:  [ -1, 5)

           n=1                                                      

 

 

 

 

8.

 

 

Use a Taylor or Maclaurin series to calculate   ln(1.1) to within accuracy 0.001.

(You may leave your answer as a fraction.)

 

Answer:  286/3000

 

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