\(\text { Tính giới hạn } L=\lim \text { . }\)

* Hướng dẫn giải

\(L=\lim \frac{\left(n^{2}+2 n\right)\left(2 n^{3}+1\right)(4 n+5)}{\left(n^{4}-3 n-1\right)\left(3 n^{2}-7\right)}=\lim \frac{\left(1+\frac{2}{n}\right)\left(2+\frac{1}{n^{3}}\right)\left(4+\frac{5}{n}\right)}{\left(1-\frac{3}{n^{3}}-\frac{1}{n^{4}}\right)\left(3-\frac{7}{n^{2}}\right)}=\frac{1.2 .4}{1.3}=\frac{8}{3}\)