Chapter 11.2, Problem 76E

a.

To determine

To show: The remainder of Taylor series is $R_n\left(x\right)=\frac{x^n}{\left(1-x\right)}$.

b.

To determine

To sketch: The remainder functions on the interval $\left|x\right|<1$ and interpret the interval is $\left|R_n\left(x\right)\right|$ largest and smallest.

c.

To determine

To check: Whether the result agrees with the observation in part (b).

d.

To determine

To sketch: The function $N\left(x\right)$ on the interval $\left|x\right|<1$.