# Question #c3fab

Jun 5, 2017

The limit does not exist.

#### Explanation:

Suppose we look at the function $f \left(x\right)$

$f \left(x\right) = \frac{\left\mid {x}^{3} + 2 {x}^{2} + 5 x - 26 \right\mid}{3 x - 6}$

It's graph looks like this

graph{(abs(x^3+2x^2+5x-26))/(3x-6)[-15,15,-50,50]}

At $x = 2$, we have a discontinuity.

The limit as $x \to {2}^{-}$ from the left approaches $- \frac{25}{3} = - 8.3 \overline{3}$.

The limit as $x \to {2}^{+}$ from the right approaches $\frac{25}{3} = + 8.3 \overline{3}$.

Because approaches two different numbers, from the left and right, the limit does not exist.

Jun 5, 2017

The limit does not exist because the graph is discontinuous at $x = 2$