Chapter 11.1, Problem 85E

a.

To determine

The Taylor series for $p_5$ and $q_5$.

b.

To determine

To sketch: The function f, the Taylor polynomials $p_5$ and $q_5$.on the interval $\left[-\pi ,2\pi \right]$ and to find which interval $p_5$ better approximation to f than $q_5$ and which interval $q_5$ better approximation to f than $p_5$.

c.

To determine

The error approximation of $\left|\sin x-p_5\left(x\right)\right|$ and $\left|\sin x-q_5\left(x\right)\right|$.

d.

To determine

The point from the given table such that $p_5\left(x\right)$ is better approximation to f than $q_5\left(x\right)$ as well as comparable approximation between them and comments on that approximations.