Đáp án:
\(2)\dfrac{{ - 3}}{{2 + \sqrt 3 }}\)
Giải thích các bước giải:
\(\begin{array}{l}
1)\mathop {\lim }\limits_{x \to + \infty } \dfrac{{\sqrt {\dfrac{2}{x} + \dfrac{7}{{{x^2}}}} - 3}}{{2 - \sqrt {3 + \dfrac{1}{{{x^2}}}} }} = \mathop {\lim }\limits_{x \to + \infty } \dfrac{{ - 3}}{{2 - \sqrt 3 }} = \dfrac{{ - 3}}{{2 - \sqrt 3 }}\\
2)\mathop {\lim }\limits_{x \to - \infty } \dfrac{{ - \sqrt {\dfrac{2}{x} + \dfrac{7}{{{x^2}}}} - 3}}{{2 - \left( { - \sqrt {3 + \dfrac{1}{{{x^2}}}} } \right)}} = \mathop {\lim }\limits_{x \to - \infty } \dfrac{{ - 3}}{{2 + \sqrt 3 }} = \dfrac{{ - 3}}{{2 + \sqrt 3 }}
\end{array}\)
