Chapter 11.1, Problem 37E

To determine

To find: the limit of the given function

Answer to Problem 37E

The limit is not defined.

Explanation of Solution

Given:

  $\underset{x\to 1}{\lim }\frac{1}{x-1}$

  

Calculation:

  $\underset{x\to 1}{\lim }\frac{1}{x-1}=\frac{1}{1-1}=\frac{1}{0}=\text{ undefined}$

From the graph provided, the function decreases without bound as $x\to 1$ from the negative direction and grows without bound as $x\to 1$ from the positive direction. Therefore the limit is not defined.

Conclusion:

Therefore, the limit is not defined.