\(\mathop {\lim }\limits_{x \to - 2} \frac{{\sqrt {{x^2} + 5} - 3}}{{x + 2}}\) bằng
A. 0 | B. 1 | C. \( - \frac{2}{3}\) | D. |
\(\begin{array}{l}
\mathop {\lim }\limits_{x \to - 2} \frac{{\sqrt {{x^2} - 5} - 3}}{{x + 2}} = \mathop {\lim }\limits_{x \to - 2} \frac{{\left( {{x^2} + 5} \right) - 9}}{{\left( {x + 2} \right)\left( {\sqrt {{x^2} + 5} + 3} \right)}}\\
= \mathop {\lim }\limits_{x \to - 2} \frac{{{x^2} - 4}}{{\left( {x + 2} \right)\left( {\sqrt {{x^2} + 5} + 3} \right)}} = \mathop {\lim }\limits_{x \to - 2} \frac{{x - 2}}{{\sqrt {{x^2} + 5} + 3}} = - \frac{2}{3}
\end{array}\)
Đáp án : C
-- Mod Toán 11