Ta xét
$\underset{x \to a}{\lim} \dfrac{\sqrt{x^2 + 3a^2} - 2a}{x-a} = \underset{x \to a}{\lim} \dfrac{x^2 + 3a^2 - 4a^2}{(x-a)(\sqrt{x^2 + 3a^2} + 2a)}$
$= \underset{x \to a}{\lim} \dfrac{(x-a)(x+a)}{(x-a)(\sqrt{x^2 + 3a^2} + 2a)}$
$= \underset{x \to a}{\lim} \dfrac{x+a}{\sqrt{x^2 + 3a^2} + 2a}$
$= \dfrac{2a}{2a + 2a} = \dfrac{1}{2}$
Vậy
$\underset{x \to a}{\lim} \dfrac{\sqrt{x^2 + 3a^2} - 2a}{x-a} = \dfrac{1}{2}$.
