Đáp án:
$\begin{array}{l}
2)\lim \frac{{{{2.7}^n} + {5^n}}}{{{{3.3}^n} + {7^n}}} = \lim \frac{{2 + \frac{{{5^n}}}{{{7^n}}}}}{{3.\frac{{{3^n}}}{{{7^n}}} + 1}} = \frac{{2 + 0}}{{0 + 1}} = 2\\
3)\mathop {\lim }\limits_{x \to \infty } \frac{{\sqrt {3x + 1} - 2}}{{{x^2} - 1}}\\
= \mathop {\lim }\limits_{x \to \infty } \frac{{3x + 1 - 4}}{{\left( {x + 1} \right)\left( {x - 1} \right)\left( {\sqrt {3x + 1} + 2} \right)}}\\
= \mathop {\lim }\limits_{x \to \infty } \frac{{3x - 3}}{{\left( {x + 1} \right)\left( {x - 1} \right)\left( {\sqrt {3x + 1} + 2} \right)}}\\
= \mathop {\lim }\limits_{x \to \infty } \frac{3}{{\left( {x + 1} \right)\left( {\sqrt {3x + 1} + 2} \right)}}\\
= \mathop {\lim }\limits_{x \to \infty } \frac{{\frac{3}{{x\sqrt x }}}}{{\left( {1 + \frac{1}{x}} \right)\left( {\sqrt {3 + \frac{1}{x}} + \frac{2}{{\sqrt x }}} \right)}}\\
= 0
\end{array}$
