Answer
the limit does not exist
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 4, which is positive.
The denominator, however, has different signs when we approach -2 from different sides.
Evaluate for -1.99 (denom.=-0.0099$) $and -2.01 (denom=+0.0101) to confirm.
The limit takes the determinate form $\displaystyle \frac{k}{0^{\pm}}=\pm\infty $,
but one side diverges to $-\infty$, and the other to $+\infty$, so
the limit does not exist
