Chapter 11.2, Problem 36E

To determine

To find: the value of the limit.

Answer to Problem 36E

The value of the limit is $\underset{x\to \pi }{\lim }\frac{1+\cos x}{x}=0$

Explanation of Solution

Given:

  $\underset{x\to \pi }{\lim }\frac{1+\cos x}{x}$

Calculation:

  $\underset{x\to \pi }{\lim }\frac{1+\cos x}{x}=\frac{1-1}{\pi }=0$

Verify this by inspecting the graph of the function around $x=\pi$ .

  

Conclusion:

The limit is $\underset{x\to \pi }{\lim }\frac{1+\cos x}{x}=0$