Chapter 14.3, Problem 50AYU

To determine

To find: Whether $f$ is continuous at $c$.

Answer to Problem 50AYU

Not continuous.

Explanation of Solution

Given:

$f\left(x\right)=\frac{x-6}{x+6}$; $c=-6$

Calculation:

We see that,

$\underset{x\to c}{\lim }f\left(x\right)=\underset{x\to -6}{\lim }\left(\frac{x-6}{x+6}\right)=\frac{-6-6}{-6+6}=\frac{-12}{0}$; does not exist (undefined).

Since $\underset{x\to c}{\lim }f\left(x\right)$ is undefined, therefore $f$ is not continuous at $c$.