Answer
$\dfrac{1}{4}$
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
In order to to find the limit, we will plug $ a $ into the function and then simplify.
$\lim_\limits{x\to 4} \dfrac{\sqrt x-2}{x-4}=\lim_\limits{x\to 4} \dfrac{1}{\sqrt x+2}$
or, $= \dfrac{1}{\sqrt 4+2}$
or, $= \dfrac{1}{4}$
