Question

Lim x>-1 (x+1)^3/ (x+3căn3(x^2)+3căn3(x)+1)

Answer 1

\(\lim\limits_{x\rightarrow-1}\dfrac{\left(x+1\right)^3}{x+3\sqrt[3]{x^2}+3\sqrt[3]{x}+1}\\ =\lim\limits_{x\rightarrow-1}\dfrac{\left(x+1\right)^3}{\left(\sqrt[3]{x}+1\right)^3}\\ =\lim\limits_{x\rightarrow-1}\dfrac{\left(\sqrt[3]{x}+1\right)^3\left(\sqrt[3]{x^2}-\sqrt[3]{x}+1\right)^3}{\left(\sqrt[3]{x}+1\right)^3}\\ =\lim\limits_{x\rightarrow-1}\left(\sqrt[3]{x^2}-\sqrt[3]{x}+1\right)^3=3^3=27\)