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Math Help - Rewriting expression with a limit

  1. #1
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    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...
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  2. #2
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    Re: Rewriting expression with a limit

    Quote Originally Posted by Lepzed View Post
    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}}=~?
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  3. #3
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    Re: Rewriting expression with a limit

    Noted and this particular number is chosen to remove the root from the numerator?
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    Re: Rewriting expression with a limit

    Quote Originally Posted by Lepzed View Post
    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?
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    Re: Rewriting expression with a limit

    That the limit goes to infinity and that function is not differentiable in that point
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    Re: Rewriting expression with a limit

    Quote Originally Posted by Lepzed View Post
    That the limit goes to infinity and that function is not differentiable in that point
    Correct
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    Re: Rewriting expression with a limit

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