Question #c3fab

2 Answers
Jun 5, 2017

The limit does not exist.

Explanation:

Suppose we look at the function f(x)

f(x)=(abs(x^3+2x^2+5x-26))/(3x-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->2^(-) from the left approaches -25/3=-8.3bar3.

The limit as x -> 2^+ from the right approaches 25/3=+8.3bar3.

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