Tính: \(\mathop {\lim }\limits_{x \to - \infty } \frac{{\sqrt {4{x^2} + 1} - 3x}}{{x - 2}}\).

* Hướng dẫn giải

\(\mathop {\lim }\limits_{x \to  - \infty } \dfrac{{\sqrt {4{x^2} + 1}  - 3x}}{{x - 2}} = \mathop {\lim }\limits_{x \to  - \infty } \dfrac{{ - x\sqrt {4 + \dfrac{1}{{{x^2}}}}  - 3x}}{{x\left( {1 - \dfrac{2}{x}} \right)}} = \mathop {\lim }\limits_{x \to  - \infty } \dfrac{{ - \sqrt {4 + \dfrac{1}{{{x^2}}}}  - 3}}{{\left( {1 - \dfrac{2}{x}} \right)}} =  - 5\) .

Chọn A.