Question #61305

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Answer 1 · 2017-09-11T02:32:34

The fraction can be simplified as

$(x+6)/(x^2-36)=(x+6)/[(x-6)*(x+6)]=1/(x-6)$

Hence the limit is

$lim_(x->6^-) 1/(x - 6) = -oo$

and

$lim_(x->6^+) 1/(x - 6) = +oo$

Hence the limit does not exist.

A graph around $x=6$ is as follows

enter image source here