Chapter 9.7, Problem 45ES

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.

$f(x)=\frac{1}{1+x^2};p(x)=1-x^2+x^4$