# How do you prove that the function f(x) = [x^2 + x] / [x] is not continuous at a =0?

May 9, 2018

Check below

#### Explanation:

$f$ is not continuous at $0$ because $0$ $\cancel{\in}$${D}_{f}$

The domain of $\frac{{x}^{2} + x}{x}$ is $\mathbb{R}$* $= \mathbb{R} - \left\{0\right\}$

May 9, 2018

Expression undefined; $0$ in denominator

#### Explanation:

Let's plug in $0$ for $x$ and see what we get:

$\frac{0 + 0}{0} = \textcolor{b l u e}{\frac{0}{0}}$

What I have in blue is indeterminate form. We have a zero in a denominator, which means this expression is undefined.

Hope this helps!