Chapter 11.4, Problem 65E

a.

To determine

Whether the statement “the value of ${\displaystyle \underset{0}{\overset{2}{\int }}\frac{dx}{1-x}}$ can be expanded in a Taylor series and can be integrated term by term” is true or false.

b.

To determine

Whether the statement “The substitution of $x=\sqrt{3}$ into the Taylor series for ${\tan }^{-1}x$ approximates $\frac{\pi }{3}$” is true or false.

c.

To determine

Whether the statement “ ${\displaystyle \sum _{k=0}^{\infty }\frac{{\left(\ln 2\right)}^k}{k!}}=2$” is true or false.