Đáp án:
$\mathop {\lim }\limits_{x \to 6 } \dfrac{\sqrt{x+3}-3}{x-6} = \dfrac{1}{6}$
Giải thích các bước giải:
$\mathop {\lim }\limits_{x \to 6 } \dfrac{\sqrt{x+3}-3}{x-6}$
$\mathop {\lim }\limits_{x \to 6 } \dfrac{(\sqrt{x+3}-3)(\sqrt{x+3}+3)}{(x-6)(\sqrt{x+3}+3)}$
$\mathop {\lim }\limits_{x \to 6 } \dfrac{x+3-9}{(x-6)(\sqrt{x+3}+3)}$
$\mathop {\lim }\limits_{x \to 6 } \dfrac{x-6}{(x-6)(\sqrt{x+3}+3)}$
$\mathop {\lim }\limits_{x \to 6 } \dfrac{1}{\sqrt{x+3}+3}$
$\mathop {\lim }\limits_{x \to 6 } \dfrac{1}{3+3}$
$\mathop {\lim }\limits_{x \to 6 } = \dfrac{1}{6}$
