A function is said to have a vertical asymptote wherever the limit on the left or right (or both) is either positive or negative infinity.
For example, the function $\displaystyle{f(x)=\frac{-3\!\left(x+2\right)}{x^{2}+4x+4}}$ has a vertical asymptote at $x=-2$.

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Find each of the following limits.

$\displaystyle{ \lim_{x\to -2^-}\frac{-3\!\left(x+2\right)}{x^{2}+4x+4}= }$ help (limits)

$\displaystyle{ \lim_{x\to -2^+}\frac{-3\!\left(x+2\right)}{x^{2}+4x+4}=}$ help (limits)

$\displaystyle{ \lim_{x\to -2}\frac{-3\!\left(x+2\right)}{x^{2}+4x+4}=}$ help (limits)