Chapter 14.3, Problem 49AYU

$f\left(x\right)=\frac{x+3}{x-3}c=3$

To determine

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

Answer to Problem 49AYU

Not continuous.

Explanation of Solution

Given:

$f\left(x\right)=\frac{x+3}{x-3}$; $c=3$

Calculation:

We see that,

$\underset{x\to c}{\lim }f\left(x\right)=\underset{x\to 3}{\lim }\left(\frac{x+3}{x-3}\right)=\frac{3+3}{3-3}=\frac{6}{0}$; does not exist (undefined).

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