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Question Number 158894 by mathlove last updated on 10/Nov/21

Commented by cortano last updated on 10/Nov/21

$$\underset{x\to y}{\lim }\frac{{\left(\sqrt[3]{x}\right)}^2-{\left(\sqrt[3]{y}\right)}^2}{x-y}$$$$=\underset{x\to y}{\lim }\frac{(\sqrt[3]{x}+\sqrt[3]{y})(\sqrt[3]{x}-\sqrt[3]{y})}{(\sqrt[3]{x}-\sqrt[3]{y})(\sqrt[3]{x^2}+\sqrt[3]{xy}+\sqrt[3]{y})}$$$$=\frac{2\sqrt[3]{y}}{3\sqrt[3]{y^2}}=\frac{2}{3\sqrt[3]{y}}$$

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