Chapter 9.9, Problem 13ES

(a) Use the Maclaurin series for ${\text{tan}}^{-\text{1}}x$ to approximate $\text{tan}{}^{-1}x$ to approximate ${\tan }^{-1}\frac{1}{2}$ and ${\tan }^{-1}\frac{1}{3}$ to three decimal-place accuracy.

(b) Use the results in part (a) and Formula (16) to approximate $\pi .$

(c) Would you be willing to guarantee that your answer in part (b) is accurate to three decimal places? Explain your reasoning.

(d) Compare your answer in part (b) to that produced by your calculating utility.