Chapter 9, Problem 15RE

To determine

To Find the limit.

Answer to Problem 15RE

The solution is $\text{'}0\text{'}$

Explanation of Solution

Given information:

Given equation is,

  $\underset{r\to \infty }{\lim }\frac{\cos r}{\ln r}$

CALCULATION:

The limit of the expression is obtained as:

  $\begin{array}{l}=\underset{r\to \infty }{\lim }\frac{\cos r}{\ln r}\\ =\underset{r\to \infty }{\lim }\frac{1}{\ln r}\left[-1\le \cos r\le 1\text{ for}\text{all }\pi \right]\\ =\underset{r\to \infty }{\lim }\frac{-1}{\ln r}=0\\ \text{so,}\frac{\cos r}{\ln r}=0\text{also,}\end{array}$

Hence,

The solution is $\text{'}0\text{'}$