\(\text { Kết quả của giới hạn } \lim \frac{2 n+3 n^{3}}{4 n^{2}+2 n+1} \text { là: }\)

* Hướng dẫn giải

\(\lim \frac{2 n+3 n^{3}}{4 n^{2}+2 n+1}=\lim \frac{n^{3}\left(\frac{2}{n^{2}}+3\right)}{n^{2}\left(4+\frac{2}{n}+\frac{1}{n^{2}}\right)}=\lim n \cdot \frac{\frac{2}{n^{2}}+3}{4+\frac{2}{n}+\frac{1}{n^{2}}} .\)

Ta có

\(\left\{\begin{array}{l} \lim n=+\infty \\ \lim \frac{\frac{2}{n^{2}}+3}{4+\frac{2}{n}+\frac{1}{n^{2}}}=\frac{3}{4}>0 \end{array}\right.\)\(\longrightarrow \operatorname{lim} \frac{2 n+3 n^{3}}{4 n^{2}+2 n+1}=\lim n \cdot \frac{\frac{2}{n^{2}}+3}{4+\frac{2}{n}+\frac{1}{n^{2}}}=+\infty .\)