- #1

quasar987

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Evaluate

[tex]\lim_{x\rightarrow 1}\frac{\sqrt[3]{x}-1}{x-1} [/tex]

This is an indeterminate form [itex]\frac{0}{0}[/itex]. Let's multiply by the conjugate 2 times.

[tex]\lim_{x\rightarrow 1}\frac{\sqrt[3]{x}-1}{x-1} = \lim_{x\rightarrow 1}\frac{\sqrt[3]{x}-1}{x-1} \frac{\sqrt[3]{x}+1}{\sqrt[3]{x}+1}\frac{\sqrt[3]{x}+1}{\sqrt[3]{x}+1} = \lim_{x\rightarrow 1}\frac{(x-1)+\sqrt[3]{x^2}-\sqrt[3]{x}}{(x-1)(\sqrt[3]{x}+1)^2}[/tex]

I have tried going farther, setting [itex]y = \sqrt[3]{x}[/itex] but it's not coming to anything.