Tìm giới hạn lim x→1 3√x−1/x^2−1.

Question

Tìm giới hạn \({\mathop{\lim }\limits_{x\to 1}} \frac{\sqrt[{3}]{x} -1}{x^{2} -1} .\)

\(A. 0\).

\(B. \frac{1}{6} . \)

\(C. \frac{1}{3} \).

\(D. \frac{1}{2} .\)

Answer 1

Chọn B
\({\mathop{\lim }\limits_{x\to 1}} \frac{\sqrt[{3}]{x} -1}{x^{2} -1} ={\mathop{\lim }\limits_{x\to 1}} \frac{x-1}{\left(x^{2} -1\right)\left(\sqrt[{3}]{x^{2} } +\sqrt[{3}]{x} +1\right)} ={\mathop{\lim }\limits_{x\to 1}} \frac{1}{\left(x+1\right)\left(\sqrt[{3}]{x^{2} } +\sqrt[{3}]{x} +1\right)} =\frac{1}{6} . \)