Answer
$\dfrac{1}{4}$
Work Step by Step
Consider: $\lim\limits_{x \to 2}f(x)=\lim\limits_{x \to 2}\dfrac{x -2}{x^2-4}$
Now, $f(2)=\dfrac{2 -2}{4-4}=\dfrac{0}{0}$
The limit shows an indeterminate form. Thus, apply L-Hospital's rule: $\lim\limits_{a \to b}f(x)=\lim\limits_{a \to b}\dfrac{g'(x)}{h'(x)}$
Thus:
$\lim\limits_{x \to 2}\dfrac{1}{2x}=\dfrac{1}{2(2)}=\dfrac{1}{4}$
