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