Chapter 1.2, Problem 11ES

a.

To determine

The approximate error and relative error in the approximation of $\pi$ for $4\left({\tan }^{-1}\left(\frac{1}{2}\right)+{\tan }^{-1}\left(\frac{1}{3}\right)\right)$.

b.

To determine

The approximate error and relative error in the approximation of $\pi$ for $\left(16{\tan }^{-1}\left(\frac{1}{5}\right)-4{\tan }^{-1}\left(\frac{1}{239}\right)\right)$.