Answer
$\frac{1}{3}$
Work Step by Step
$\lim\limits_{x \to 1}$ $\frac{\sqrt[3] x-1}{x-1}$
= $\lim\limits_{x \to 1}$ $\frac{\sqrt[3] x-1}{(\sqrt[3] x-1)(\sqrt[3] x^{2}+\sqrt[3] x+1)}$
= $\lim\limits_{x \to 1}$ $\frac{1}{(\sqrt[3] x^{2}+\sqrt[3] x+1)}$
= $\frac{1}{(\sqrt[3] 1^{2}+\sqrt[3] 1+1)}$
= $\frac{1}{(1+1+1)}$
=$\frac{1}{3}$
