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Answer 1 · 2016-04-03T18:27:59

Take side limits you get

#lim_(x->3^+) (x^3-8) / (x^2+x-12)=+oo#

and

#lim_(x->3^-) (x^3-8) / (x^2+x-12)=-oo#

Hence side-limits are different the limit does not exist.

The graph of f(x) near x=3 is

enter image source here