Answer
$\lim\limits_{x \to \ -1}\frac{x^2+3x}{x^2-x-2}=\frac{(-1)^2+3(-1)}{(-1)^2-(-1)-2}=\frac{-2}{0}$
Therefore we can state that the limit is not defined.
Work Step by Step
If we want to calculate the value of $\lim\limits_{x \to \ -1}\frac{x^2+3x}{x^2-x-2}$,
Here, we can use the formula of:
$\lim \limits_{x\to a}f(x)=f(a)$, meaning that:
$\lim\limits_{x \to \ -1}\frac{x^2+3x}{x^2-x-2}=\frac{(-1)^2+3(-1)}{(-1)^2-(-1)-2}=\frac{-2}{0}$
Therefore we can state that the limit is not defined.
