Chapter 11, Problem 37RE

(a)

To determine

The fifth Taylor polynomial of $f\left(x\right)=\sin x^2$ at $x=0$ using sixth Taylor polynomial, which is $x^2-\frac{x^6}{6}$

(b)

To determine

The value of $f"\text{'}\left(0\right)$, where $f\left(x\right)=\sin x^2$ at $x=0$ using the sixth Taylor polynomial which is $x^2-\frac{x^6}{6}$

(c)

To determine

The area under the graph of $y=\sin x^2$ between $x=0$ and $x=1$ using the sixth Taylor polynomial which is $x^2-\frac{x^6}{6}$ and compare the answer with the exact value $0.3103$.