Chapter 9.7, Problem 5QCE

(a) If a function f has nth Tylor polynomial $p_n\left(x\right)$ about $x=x_0$ , then the nth remainder $R_n\left(x\right)$ is defined by $R_n\left(x\right)=\text{\_\_\_\_\_\_\_}\text{.}$

(b) Suppose that a friction f can be differentiated five times on an interval containing the number $x_0=2$ and that $\left|f^{\left(5\right)}\left(x\right)\right|\le 20$ for all x in the interval. Then the fourth remainder satisfies $\left|R_4\left(x\right)\right|\le \text{\_\_\_\_\_\_}$ for all x in the interval.