Question

Alguém para me  ajudar.
segue a imagem abaixo.

Answer 1

$\lim_{x \to 2} \dfrac{ \sqrt[3]{x} - \sqrt[3]{2} }{x-2}$

$\lim_{x \to 2} \dfrac{ \sqrt[3]{x} - \sqrt[3]{2} }{ ( \sqrt[3]{x})^{3} - (\sqrt[3]{2})^{3} }$

$\lim_{x \to 2} \dfrac{ \sqrt[3]{x} - \sqrt[3]{2} }{ [ \sqrt[3]{x} - \sqrt[3]{2}].[ ( \sqrt[3]{x})^{2} + \sqrt[3]{x}.\sqrt[3]{2} + (\sqrt[3]{2} )^{2} ] }$

$\lim_{x \to 2} \dfrac{ 1 }{ ( \sqrt[3]{x})^{2} + \sqrt[3]{x}.\sqrt[3]{2} + (\sqrt[3]{2} )^{2} }$$=\dfrac{ 1 }{ ( \sqrt[3]{2})^{2} + \sqrt[3]{2}.\sqrt[3]{2} + (\sqrt[3]{2} )^{2} }=\dfrac{ 1 }{ \sqrt[3]{4}+ \sqrt[3]{4} + \sqrt[3]{4}} =\dfrac{ 1 }{ 3\sqrt[3]{4}}=\dfrac{ 1. \sqrt[3 ]{2} }{ 3\sqrt[3]{ 2^{2} }. \sqrt[3]{2} }$$=\dfrac{ \sqrt[3 ]{2} }{ 3\sqrt[3]{ 2^{3} } } =\dfrac{ \sqrt[3]{2} }{ 3.2 } } =\dfrac{ \sqrt[3]{2} }{ 6} }$