# Math Help - Rewriting expression with a limit

1. ## 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...

2. ## Re: Rewriting expression with a limit

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

3. ## Re: Rewriting expression with a limit

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

4. ## Re: Rewriting expression with a limit

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?

5. ## Re: Rewriting expression with a limit

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

6. ## Re: Rewriting expression with a limit

Originally Posted by Lepzed
That the limit goes to infinity and that function is not differentiable in that point
Correct

7. ## Re: Rewriting expression with a limit

I am speechless. This is a fantastic site and very engaging too.agriculture Articles Excellent work! That’s not really much coming from an amateur publisher like me, but it’s all I could think after enjoying your posts. Great grammar and vocabulary. Not like other site. You really know what you’re talking about too. So much that you made me want to explore more. Business DirectoryYour blog has become a stepping stone for me, my friend. Thanks for the detailed journey. I really enjoyed the posts that I have read so far.