\(\text { Tính giới hạn } L=\lim \frac{\left(2 n-n^{3}\right)\left(3 n^{2}+1\right)}{(2 n-1)\left(n^{4}-7\right)}\)

* Hướng dẫn giải

\(L=\lim \frac{\left(2 n-n^{3}\right)\left(3 n^{2}+1\right)}{(2 n-1)\left(n^{4}-7\right)}=\lim \frac{n^{3}\left(\frac{2}{n^{2}}-1\right) \cdot n^{2}\left(3+\frac{1}{n^{2}}\right)}{n\left(2-\frac{1}{n}\right) \cdot n^{4}\left(1-\frac{7}{n^{4}}\right)}=\lim \frac{\left(\frac{2}{n^{2}}-1\right)\left(3+\frac{1}{n^{2}}\right)}{\left(2-\frac{1}{n}\right)\left(1-\frac{7}{n^{4}}\right)}=\frac{-1.3}{2.1}=-\frac{3}{2}\)