Chapter 9.9, Problem 15ES

(a) Find an upper bound on the error that can result if $\cos x$ is approximated by $1-(x^2/2!)+(x^4/4!)$ over the interval $[-0.2,0.2].$

(b) Check your answer in part (a) by graphing $\left|\cos x-\left(1-\frac{x^2}{2!}+\frac{x^4}{4!}\right)\right|$ over the interval.