Answer
the limit diverges to +$\infty$.
Work Step by Step
1. f is a closed function (we know by Th.10.1 that it is continuous), that is, L= $\displaystyle \lim_{x\rightarrow a}f(x)$ = $f(a)$,
for all a from the domain of f.
2. evaluating: $f(2)$, (plugging $x=2$) , we see that $x=2$ is NOT in the domain of f.
As $x\rightarrow 2,$ (we approach $2$ from either side),
the numerator approaches $12$, which is positive,
for the denominator , evaluating it on either side...
left: (test when x=1.99), is positive,
right: (test when x=2.01) is also positive,
so the denominator is positive regardless of the side we choose to approach 2.
The limit takes the determinate form $\displaystyle \frac{k}{0^{\pm}}=\pm\infty $, and
the limit diverges to +$\infty$.
