Chapter 6.3, Problem 168E

The following exercises make use of the functions $S_5(x)=x+\frac{x^3}{6}+\frac{x^5}{120}$ and $C_4(x)=x-\frac{x^2}{2}+\frac{x^2}{24}$ on $[-\pi ,\pi ]$ .

168. [T] Plot e^x− e₄(x) where $e_4(x)=1+x\mathrm{..}\frac{x^2}{2}+\frac{x^3}{6}+\frac{x^4}{24}$ on [0, 2]. Compare the maximum error with the Taylor remainder estimate.