Rewriting expression with a limit

I'm working through a chapter on differentiation and I don't understand how they've rewrote a certain expression:

$\displaystyle \lim_{x \to 0}\frac{\sqrt[3]{x} - \sqrt[3]{0}}{x - 0} = \lim_{x \to 0}\frac{1}{\sqrt[3]{x^2}}$. I need some step by step help on how they rewrote the left hand part to the right hand part...

Re: Rewriting expression with a limit

Quote:

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**Lepzed** I'm working through a chapter on differentiation and I don't understand how they've rewrote a certain expression:

$\displaystyle \lim_{x \to 0}\frac{\sqrt[3]{x} - \sqrt[3]{0}}{x - 0} = \lim_{x \to 0}\frac{1}{\sqrt[3]{x^2}}$. I need some step by step help on how they rewrote the left hand part to the right hand part...

Just note that $\displaystyle \frac{\sqrt[3]{x} - \sqrt[3]{0}}{x - 0}=\frac{\sqrt[3]{x} }{x }=\frac{\sqrt[3]{x} }{x }\frac{\sqrt[3]{x^2}}{\sqrt[3]{x^2}}=~?$

Re: Rewriting expression with a limit

Noted and this particular number is chosen to remove the root from the numerator?

Re: Rewriting expression with a limit

Quote:

Originally Posted by

**Lepzed** Noted and this particular number is chosen to remove the root from the numerator?

Yes, so that it can easily be seen that you have a denominator approaching 0. What does that tell you about the function?

Re: Rewriting expression with a limit

That the limit goes to infinity and that function is not differentiable in that point

Re: Rewriting expression with a limit

Quote:

Originally Posted by

**Lepzed** That the limit goes to infinity and that function is not differentiable in that point

Correct :)

Re: Rewriting expression with a limit

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