Chapter 9.7, Problem 12E

(a)

To determine

To calculate: Maclaurin polynomials $P_2,P_3\text{ and }{P}_4$ for $f.$

(b)

To determine

To graph: $f$, $P_2,P_3\text{ and }{P}_4$.

(c)

To determine

To calculate: The values of $f^{\left(n\right)}\left(0\right){\text{and P}}_n{}^{\left(n\right)}\left(0\right)$ for $n=2,3\text{ and }4$ and comparing them.

(d)

To determine

A conjecture about $f^{\left(n\right)}\left(0\right){\text{and P}}_n{}^{\left(n\right)}\left(0\right)$ using the result in the part (c).