[itex]\lim_{x \to 0}[/itex] x^(1/3)(adsbygoogle = window.adsbygoogle || []).push({});

I know that [itex]\delta = {\epsilon}^3[/itex]

the book gives an example:

[itex]\lim_{x \to 2}[/itex] (3x - 2) = 4 and you chose [itex]\delta = \frac{\epsilon}{3}[/itex]

so

0 < |x-2| < [itex]\delta = \frac{\epsilon}{3}[/itex]

implies

|(3x - 2) - 4| = 3|x-2| < [itex]3 (\frac{\epsilon}{3}) = \epsilon[/itex]

so i should get something like:

[itex] | \sqrt[3]{x} - 0 | = | x - 0 | = \epsilon[/itex]

But I don't see how you make the connection between [itex] | \sqrt[3]{x} |[/itex] and (|x - 0|) < [itex]\delta[/itex] and I don't see how I can reduce [itex]{\epsilon}^3[/itex] to just epsilon using this style of proof.

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# Delta-epsilon proof (book example)

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