Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

a. To evaluate# , one could expand the integrand in a Taylor series and integrate term by term.

b. To approximate π/3, one could substitute into the Taylor series for tan−1 x.

c. .

Solution 59E

Step 1:

(a)

Given statement is true

We have the integral is not defined that is diverges

To evaluate , one could expand the integrand in a Taylor series and integrate term by term.

Here the integrand is

The taylor series of is given by

Therefore

It is also diverges

Step 2:

(b)given Statement is true

To approximate π/3, one could substitute into the Taylor series for .

We know the Taylor series of . is given by

=

Hence .