Đáp án: 6
Giải thích các bước giải:
$\begin{array}{l}
\lim \frac{{3{n^3}.{{\left( {2n + 1} \right)}^{10}}}}{{{{\left( {2{n^2} - 1} \right)}^4}.{{\left( {2n - 3} \right)}^5}}}\\
= \lim \frac{{\frac{{3{n^3}.{{\left( {2n + 1} \right)}^{10}}}}{{{n^{13}}}}}}{{\frac{{{{\left( {2{n^2} - 1} \right)}^4}.{{\left( {2n - 3} \right)}^5}}}{{{n^{13}}}}}}\\
= \lim \frac{{3.{{\left( {\frac{{2n + 1}}{n}} \right)}^{10}}}}{{{{\left( {\frac{{2{n^2} - 1}}{{{n^2}}}} \right)}^4}.{{\left( {\frac{{2n - 3}}{n}} \right)}^5}}}\\
= \lim \frac{{3.{{\left( {2 - \frac{1}{n}} \right)}^{10}}}}{{{{\left( {2 - \frac{1}{{{n^2}}}} \right)}^4}.{{\left( {2 - \frac{3}{n}} \right)}^5}}}\\
= \frac{{{{3.2}^{10}}}}{{{2^4}{{.2}^5}}}\\
= 3.2\\
= 6
\end{array}$
