Chapter 9.7, Problem 35E

(a)

To determine

The Maclaurin polynomials $P_1\left(x\right),P_3\left(x\right),P_5\left(x\right)$ for the function, $f\left(x\right)=\sin x$ to complete the table,

x	0	0.25	0.50	0.75	1
$\sin x$	0	0.2474	0.4794	0.6816	0.8415
$P_1\left(x\right)$
$P_3\left(x\right)$
$P_5\left(x\right)$

(b)

To determine

To graph: The function $f\left(x\right)=\sin x$ and $P_1\left(x\right),P_3\left(x\right),P_5\left(x\right)$ by the use of graphing calculator.

(c)

To determine

The change in accuracy of polynomial approximations as the distance from the point where polynomial centered increases.