Đáp án:
$\begin{array}{l}
e)\lim \frac{{{{6.3}^n} - {4^n}}}{{{3^{n + 1}} + {4^{n + 1}}}}\\
= \lim \frac{{6.\frac{{{3^n}}}{{{4^n}}} - 1}}{{3.\frac{{{3^n}}}{{{4^n}}} + 4}}\\
= \frac{{0 - 1}}{{3 + 4}}\\
= - \frac{1}{7}\\
g)\lim \frac{{n\sqrt {{n^2} + 1} + \sqrt {{n^2} - n + 1} }}{{2n + 1}}\\
= \lim \frac{{\sqrt {{n^2} + 1} + \sqrt {1 - \frac{1}{n} + \frac{1}{{{n^2}}}} }}{{2 + \frac{1}{n}}}\\
= \infty \\
g)\lim \left( {n + 1} \right).\sqrt {\frac{{n - 2}}{{{n^3} - n + 3}}} \\
= \lim \sqrt {\frac{{{{\left( {n + 1} \right)}^2}\left( {n - 2} \right)}}{{{n^3} - n + 3}}} \\
= \lim \sqrt {\frac{{{n^3} - 3n - 2}}{{{n^3} - n + 3}}} \\
= 1
\end{array}$
