Answer
$\dfrac{1}{20}$
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.
$\lim_\limits {x \to 100} \dfrac{\sqrt x-10}{(\sqrt{x}+10)(\sqrt{x}-10)}=\lim_\limits {x \to 100} \dfrac{1}{(\sqrt{x}+10)}$
or, $=\dfrac{1}{20}$
