Giá trị của \(D = \lim \left( {\sqrt {{n^2} + 2n} - \sqrt[3]{{{n^3} + 2{n^2}}}} \right)\) bằng:

* Hướng dẫn giải

\(\begin{array}{l}
D = \lim \left( {\sqrt {{n^2} + 2n}  - \sqrt[3]{{{n^3} + 2{n^2}}}} \right)\\
 = \lim \left( {\sqrt {{n^2} + 2n}  - n} \right) - \lim \frac{{2{n^2}}}{{\sqrt[3]{{{{\left( {{n^3} + 2{n^2}} \right)}^2}}} + n\sqrt[3]{{{n^3} + 2{n^2}}} + {n^2}}}\\
 = \lim \frac{2}{{\sqrt {1 + \frac{2}{n}}  + 1}} - \lim \frac{2}{{\sqrt[3]{{{{\left( {1 + \frac{2}{n}} \right)}^2}}} + \sqrt[3]{{1 + \frac{2}{n}}} + 1}} = \frac{1}{3}
\end{array}\)