Question

ПОМОГИТЕ С ПРИМЕРОМ!!!!!!!!

Answer 1

$\lim_{x \to-2} \frac{\sqrt{x+7}-\sqrt{3-x}}{x+2}= \lim_{x \to-2} \frac{(\sqrt{x+7}-\sqrt{3-x})(\sqrt{x+7}+\sqrt{3-x})}{(x+2)(\sqrt{x+7}+\sqrt{3-x})}= \\ = \lim_{x \to-2} \frac{x+7-(3-x)}{(x+2)(\sqrt{x+7}+\sqrt{3-x})}= 2\lim_{x \to-2} \frac{x+2}{(x+2)(\sqrt{x+7}+\sqrt{3-x})}= \\ = \frac{2}{\sqrt{5}+\sqrt{5}}= \frac{1}{\sqrt{5}}$