# Rewriting expression with a limit

• July 22nd 2012, 12:53 PM
Lepzed
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:

$\lim_{x \to 0}\frac{\sqrt[3]{x} - \sqrt[3]{0}}{x - 0} = \lim_{x \to 0}\frac{1}{\sqrt[3]{x^2}}$. I need some step by step help on how they rewrote the left hand part to the right hand part...
• July 22nd 2012, 01:01 PM
Plato
Re: Rewriting expression with a limit
Quote:

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

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

Just note that $\frac{\sqrt[3]{x} - \sqrt[3]{0}}{x - 0}=\frac{\sqrt[3]{x} }{x }=\frac{\sqrt[3]{x} }{x }\frac{\sqrt[3]{x^2}}{\sqrt[3]{x^2}}=~?$
• July 22nd 2012, 01:07 PM
Lepzed
Re: Rewriting expression with a limit
Noted and this particular number is chosen to remove the root from the numerator?
• July 22nd 2012, 07:37 PM
Prove It
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?
• July 22nd 2012, 11:51 PM
Lepzed
Re: Rewriting expression with a limit
That the limit goes to infinity and that function is not differentiable in that point
• July 23rd 2012, 03:16 AM
Prove It
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 :)
• July 24th 2012, 11:20 PM