Đáp án:
\[\lim \frac{{2{n^2} - 1}}{{n - 3{n^2}}} = - \frac{2}{3}\]
Giải thích các bước giải:
\(\begin{array}{l}
\lim \frac{{2{n^2} - 1}}{{n - 3{n^2}}}\\
= \lim \dfrac{{\frac{{2{n^2} - 1}}{{{n^2}}}}}{{\frac{{n - 3{n^2}}}{{{n^2}}}}}\\
= \lim \dfrac{{2 - \frac{1}{{{n^2}}}}}{{\frac{1}{n} - 3}}\\
\lim \frac{1}{{{n^2}}} = 0;\,\,\,\,\lim \frac{1}{n} = 0\\
\Rightarrow \lim \left( {2 - \frac{1}{{{n^2}}}} \right) = 2;\,\,\,\,\lim \left( {\frac{1}{n} - 3} \right) = - 3\\
\Rightarrow \lim \dfrac{{2 - \frac{1}{{{n^2}}}}}{{\frac{1}{n} - 3}} = \frac{2}{{ - 3}} = \frac{{ - 2}}{3}\\
\Rightarrow \lim \frac{{2{n^2} - 1}}{{n - 3{n^2}}} = - \frac{2}{3}
\end{array}\)
