Question

In Problems 45-60, determine whether $f$is continuous at $c$.

$$\begin{gathered} f\left(x\right)=\frac{x^3+3x}{x^2-3x} \\ c=0 \end{gathered}$$

Short answer

The function is not continuous

Step-by-step solution

Given information

Given function$$\begin{gathered} f\left(x\right)=\frac{x^3+3x}{x^2-3x} \\ c=0 \end{gathered}$$

Check whether the function is defined at c

Checking, we get

$f\left(0\right)=\frac{0^3+3\left(0\right)}{0^2-3\left(0\right)}$

It is not defined and there is a hole and it is not continuous