Đáp án:
\[\lim \left( {\sqrt[3]{{{n^3} - 5n + 6}} - n} \right) = 0\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\lim \left( {\sqrt[3]{{{n^3} - 5n + 6}} - n} \right)\\
= \lim \frac{{{n^3} - 5n + 6 - {n^3}}}{{{{\sqrt[3]{{{n^3} - 5n + 6}}}^2} + n.\sqrt[3]{{{n^3} - 5n + 6}} + {n^2}}}\\
= \lim \frac{{ - 5n + 6}}{{{{\sqrt[3]{{{n^3} - 5n + 6}}}^2} + n.\sqrt[3]{{{n^3} - 5n + 6}} + {n^2}}}\\
= \lim \frac{{ - \frac{5}{n} + \frac{6}{{{n^2}}}}}{{{{\sqrt[3]{{{1^3} - \frac{5}{n} + \frac{6}{{{n^2}}}}}}^2} + 1.\sqrt[3]{{{1^3} - \frac{5}{n} + \frac{6}{{{n^2}}}}} + 1}}\\
= \frac{0}{{1 + 1 + 1}} = 0
\end{array}\)
