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Math Help - What is the steps of getting result of limit of the function?

  1. #1
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    Post What is the steps of getting result of limit of the function?

    Limit[((n^2 - n)^(1/3))/(n + 2), n -> Infinity] == 0

    Why answer is equals to 0? What are the steps?
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  2. #2
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    \displaystyle \lim_{n\to\infty}\frac{n^{2/3}}{n}=\lim_{n\to\infty}\frac{1}{n^{1/3}}=\frac{1}{\infty}=0
    Last edited by dwsmith; December 11th 2010 at 10:18 AM. Reason: Corrected per Mr. Fantastic's observation
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  3. #3
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    The trick (or first step) to all these types of limit calculations is to divide the top and bottom by the highest power of n, and then use the fact

    \lim_{n\to \infty } \, \frac{1}{n^a}=0, a>0

    along with the algebra of limits, i.e. the sum, and product rules etc.
    Last edited by aukie; December 11th 2010 at 08:50 AM.
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  4. #4
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    Quote Originally Posted by dwsmith View Post
    \displaystyle \lim_{n\to\infty}\frac{n^{2/3}}{n}=\frac{1}{n^{1/3}}=\frac{1}{\infty}=0
    I hope what you meant to post is \displaystyle \lim_{n\to\infty}\frac{n^{2/3}}{n}=  \lim_{n\to\infty} \frac{1}{n^{1/3}} =0.
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