Chapter 9.7, Problem 43ES

Use the Remainder Estimation Theorem to find an interval containing $x=0$ over which $f(x)$ can be approximated by $p(x)$ to three decimal-place accuracy throughout the interval. Check your answer by graphing $\left|f(x)-p(x)\right|$ over the interval you obtained.

$f(x)=\sin x;p(x)=x-\frac{x^3}{3!}$