Chapter 8.8, Problem 55E

To determine

(a)

To check that $f\text{'}\text{'}(x)=2\cos (x^2)-4x^2\sin (x^2)$ and then show that $\left|f\text{'}\text{'}(x)\le 6\right|$ for $x\in [0,1]$ using the hint that $\left|2\cos (x^2)\right|\le 2$ and $\left|4x^2\sin (x^2)\right|\le 4$ for $x\in [0,1]$

To determine

(b)

To show that Error ($M_N$) is at most $\frac{1}{4N^2}$

To determine

(c)

An $N$such that $\left|1-M_N\right|\le {10}^{-3}$