Đáp án:
\[\mathop {\lim }\limits_{x \to 0} \frac{{1 - \sqrt[3]{{x - 1}}}}{{3x}} = \infty \]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\mathop {\lim }\limits_{x \to 0} \frac{{1 - \sqrt[3]{{x - 1}}}}{{3x}}\\
\mathop {\lim }\limits_{x \to 0} \left( {1 - \sqrt[3]{{x - 1}}} \right) = 1 - \sqrt[3]{{0 - 1}} = 1 + 1 = 2\\
\mathop {\lim }\limits_{x \to 0} \left( {3x} \right) = 3.0 = 0\\
\Rightarrow \mathop {\lim }\limits_{x \to 0} \frac{{1 - \sqrt[3]{{x - 1}}}}{{3x}} = \infty
\end{array}\)