Answer
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 the right)
the numerator approaches 12, which is positive,
and
for the denominator ,plug in a number close to -2 and evaluate
eg. for -1.99, denominator = -0.0099 .
so the denominator is negative for x slightly to the right of -2.
The limit takes the determinate form $\displaystyle \frac{k}{0^{\pm}}=\pm\infty $,
and diverges to $-\infty$
