\(\lim\limits_{x\rightarrow0}\dfrac{1-\sqrt[3]{1-x}}{2x+x^2}\)
\(=\lim\limits_{x\rightarrow0}\left(\dfrac{1-\left(1-x\right)}{1+\sqrt[3]{1-x}+\sqrt[3]{\left(1-x\right)^2}}\cdot\dfrac{1}{x\left(x+2\right)}\right)\)
\(=\lim\limits_{x\rightarrow0}\left(\dfrac{1}{\left(x+2\right)\left(1+\sqrt[3]{1-x}+\sqrt[3]{\left(1-x\right)^2}\right)}\right)\)
\(=\dfrac{1}{\left(0+2\right)\left(1+\sqrt[3]{1-0}+\sqrt[3]{\left(1-0\right)^2}\right)}\)
\(=\dfrac{1}{2\cdot3}=\dfrac{1}{6}\)
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