Answer
$2\sqrt a$
Work Step by Step
We have to determine $L=\lim\limits_{x \to a}\dfrac{x-a}{\sqrt x-\sqrt a}$, where $a>0$.
Factor the numerator using the identity:
$x^2-y^2=(x-a)(x+a)$:
$L=\lim\limits_{x \to a}\dfrac{(\sqrt x-\sqrt a)(\sqrt x+\sqrt a)}{\sqrt x-\sqrt a}$
Simplify:
$L=\lim\limits_{x \to a} (\sqrt x+\sqrt a)$
Determine $L$:
$L=\lim\limits_{x \to a} \sqrt x+\sqrt a=\sqrt a+\sqrt a=2\sqrt a$
