\(\lim_{}\left(\sqrt{n^2+2}\cdot\sqrt[3]{8n^3+1}-\sqrt{4n^2+1}\cdot\sqrt[3]{n^3+2}\right)\)
\(=\lim_{}\left(n\cdot\sqrt{1+\frac{2}{n^2}}\cdot n\cdot\sqrt[3]{8+\frac{1}{n^3}}-n\cdot\sqrt{4+\frac{1}{n^2}}\cdot n\cdot\sqrt{1+\frac{2}{n^3}}\right)\)
\(=\lim_{}\left\lbrack n^2\cdot\left(\sqrt{1+\frac{2}{n^2}}\cdot\sqrt[3]{8+\frac{1}{n^3}}+\sqrt[2]{4+\frac{1}{n^2}}\cdot\sqrt[3]{1+\frac{2}{n^3}}\right)\right\rbrack\)
=+∞ vì \(\lim_{}n^2=\) +∞ và \(\lim_{}\left(\sqrt{1+\frac{2}{n^2}}\cdot\sqrt[3]{8+\frac{1}{n^3}}+\sqrt[2]{4+\frac{1}{n^2}}\cdot\sqrt[3]{1+\frac{2}{n^3}}\right)=1\cdot\sqrt[3]{8}+\sqrt[2]{4}\cdot\sqrt[3]{1}=1\cdot2+2\cdot1=4>0\)
