Chapter 9.7, Problem 33E

Numerical and Graphical Approximations

(a) Use the Maclaurin polynomials $P_1(x),P_3(x)$, and $P_5(x)$ for $f(x)=\sin x$ to complete the table.

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

(b) Use a graphing utility to graph $f(x)=\sin x$ and the Maclaurin polynomials in part (a).

(c) Describe the change in accuracy of a polynomial approximation as the distance from the point where the polynomial is centered increases.