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Answer 1 · 2017-06-05T19:50:48

The limit does not exist.

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.

Answer 2 · 2017-06-05T23:57:58

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