Solution Found!
Explain why or why not Determine whether the
Chapter 8, Problem 59E(choose chapter or problem)
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. To evaluate \(\int_{0}^{2} \frac{d x}{1-x}\), one could expand the integrand in a Taylor series and integrate term by term.
b. To approximate \(\pi / 3\), one could substitute \(x=\sqrt{3}\) into the Taylor series for \(\tan ^{-1} x\).
c. \(\sum_{k=0}^{\infty} \frac{(\ln 2)^{k}}{k !}=2\).
Questions & Answers
QUESTION:
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. To evaluate \(\int_{0}^{2} \frac{d x}{1-x}\), one could expand the integrand in a Taylor series and integrate term by term.
b. To approximate \(\pi / 3\), one could substitute \(x=\sqrt{3}\) into the Taylor series for \(\tan ^{-1} x\).
c. \(\sum_{k=0}^{\infty} \frac{(\ln 2)^{k}}{k !}=2\).
ANSWER: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