Đáp án:
2) 0
Giải thích các bước giải:
\(\begin{array}{l}
1)\mathop {\lim }\limits_{x \to - \infty } \dfrac{{ - \sqrt {1 + \dfrac{2}{x} + \dfrac{3}{{{x^2}}}} + 4}}{{ - \sqrt {4 + \dfrac{1}{{{x^2}}}} - 1 + \dfrac{1}{x}}} = \dfrac{{ - 1 + 4}}{{ - 2 - 1}} = \dfrac{3}{{ - 3}} = - 1\\
2)\mathop {\lim }\limits_{x \to - \infty } \dfrac{{\left| x \right| + \sqrt {{x^2} + x} }}{{x + 10}}\\
= \mathop {\lim }\limits_{x \to - \infty } \dfrac{{\left| 1 \right| - \sqrt {1 + \dfrac{1}{x}} }}{{1 + \dfrac{{10}}{x}}} = \dfrac{{1 - 1}}{1} = 0\\
3)\mathop {\lim }\limits_{x \to \infty } \dfrac{{x + \sqrt {4{x^2} - x + 1} }}{{1 - 2x}}\\
= \mathop {\lim }\limits_{x \to \infty } \dfrac{{1 + \sqrt {4 - \dfrac{1}{x} + \dfrac{1}{{{x^2}}}} }}{{\dfrac{1}{x} - 2}} = \dfrac{{1 + 2}}{{ - 2}} = - \dfrac{3}{2}
\end{array}\)
