Answer
$ \dfrac{1}{6}$
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.
$\lim_\limits{x\to 9} \dfrac{\sqrt x-3}{x-9}=\lim_\limits{x\to 9} \dfrac{1}{\sqrt x+3}$
or, $= \dfrac{1}{\sqrt 9+3}$
or, $= \dfrac{1}{6}$
