Chapter 11.1, Problem 30E

(a)

To determine

To prove: The value $\left|f^3\left(c\right)\right|\le 4$ when $c\ge 0.8$, where $f\left(x\right)=\ln x$ at $x=1$

(b)

To determine

To prove: The error in using $p_2\left(0.8\right)$ as an approximation for $\ln \left(0.8\right)$ is at most $\frac{16}{3}\times {10}^{-3}<0.0054$, where $p_2\left(x\right)$ be the second Taylor polynomial of $f\left(x\right)=\ln x$ at $x=1$.