Tính \(\lim \left( {\sqrt[3]{{n + 2}} - \sqrt[3]{n}} \right)\).

* Hướng dẫn giải

\(\begin{array}{l}\lim \left( {\sqrt[3]{{n + 2}} - \sqrt[3]{n}} \right) = \lim \dfrac{{\left( {\sqrt[3]{{n + 2}} - \sqrt[3]{n}} \right)\left( {{{\sqrt[3]{{n + 2}}}^2} + \sqrt[3]{{n + 2}}\sqrt[3]{n} + {{\sqrt[3]{n}}^2}} \right)}}{{{{\sqrt[3]{{n + 2}}}^2} + \sqrt[3]{{n + 2}}\sqrt[3]{n} + {{\sqrt[3]{n}}^2}}}\\ = \lim \dfrac{{n + 2 - n}}{{{{\sqrt[3]{{n + 2}}}^2} + \sqrt[3]{{n + 2}}\sqrt[3]{n} + {{\sqrt[3]{n}}^2}}} = \lim \dfrac{2}{{{{\sqrt[3]{{n + 2}}}^2} + \sqrt[3]{{n + 2}}\sqrt[3]{n} + {{\sqrt[3]{n}}^2}}} = 0\end{array}\)

Chọn D.