Đáp án: 0
Giải thích các bước giải:
$\begin{array}{l}
\lim \left( {n - \sqrt[3]{{{n^3} + 1}}} \right)\\
= \lim \frac{{\left( {n - \sqrt[3]{{{n^3} + 1}}} \right)\left( {{n^2} + n\sqrt[3]{{{n^3} + 1}} + \sqrt[3]{{{{\left( {{n^3} + 1} \right)}^2}}}} \right)}}{{{n^2} + n.\sqrt[3]{{{n^3} + 1}} + \sqrt[3]{{{{\left( {{n^3} + 1} \right)}^2}}}}}\\
= \lim \frac{{{n^3} - {n^3} - 1}}{{{n^2} + n.\sqrt[3]{{{n^3} + 1}} + \sqrt[3]{{{{\left( {{n^3} + 1} \right)}^2}}}}}\\
= \lim \frac{{ - 1}}{{{n^2} + n.\sqrt[3]{{{n^3} + 1}} + \sqrt[3]{{{{\left( {{n^3} + 1} \right)}^2}}}}}\\
= 0.
\end{array}$
