[tex]lim \sqrt{n^{2}+n+1}+ \sqrt[3]{n^{3}+3n+2}[/tex]
[tex]=lim [\sqrt{n^{2}+n+1}-(n+1)]+ [\sqrt[3]{n^{3}+3n+2}+(n+1)][/tex] (nhân liên hợp được)
[tex]=lim \frac{-n}{\sqrt{n^{2}+n+1}+(n+1)}+ \frac{-3n^{2}+1}{\sqrt[3]{n^{3}+3n+2}^{2}-\sqrt[3]{n^{3}+3n+2}.(n+1)+(n+1)^{2}}[/tex]
[tex]=lim \frac{-1}{\sqrt{1+\frac{1}{n}+\frac{1}{n^{2}}}+(1+\frac{1}{n})}+ \frac{-3+\frac{1}{n^{2}}}{\sqrt[3]{1+\frac{3}{n^{2}}+\frac{2}{n^{3}}}^{2}-\sqrt[3]{1+\frac{3}{n^{2}}+\frac{2}{n^{3}}}.(1+\frac{1}{n})+(1+\frac{1}{n})^{2}}[/tex]
[tex]=\frac{-7}{2}[/tex]