Answer
$\dfrac{7}{12}$
Work Step by Step
Our aim is to compute the value of $\lim\limits_{x \to \ 6}\dfrac{x^2- 5x-6}{x^2-36}$.
Here, we need to use the formula of:
$\lim \limits_{x\to a}f(x)=f(a)$, this implies that:
We find that after applying direct limits we find indeterminate form $\dfrac{0}{0}$, so we will apply L-Hospital's Rule.
$\lim\limits_{x \to \ 6} \dfrac{2x- 5}{2x} = \dfrac{(2)(6)-5}{(2)(6)}\\=\dfrac{7}{12}$
