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