Question

Calcule lim x-1 raiz cubica de x+7-2/x-1

Answer 1

$\displaystyle \lim_{x\to1}\sqrt[3]{\frac{x+7}{x-1}}=\lim_{x\to1}\sqrt[3]{\frac{x+7}{x-1}}\\\\ x.(1+\frac{7}{x})=x+7\ \ \ |\ \ \ x(1-\frac{1}{x})=x-1\\\\ \lim_{x\to 1}\sqrt[]{\frac{x(1+\frac{7}{x})}{x(1-\frac{1}{x}}}=\sqrt[3]{\frac{\frac{7}{1}}{-\frac{1}{1}}}=\sqrt[3]{-\frac{7}{1}}=\sqrt[3]{-7}=-7^{\frac{1}{3}}$
acredito que seja essa a resposta