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