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Thread: What is the steps of getting result of limit of the function?

  1. December 10th 2010, 03:50 PM #1
    RCola
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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. December 10th 2010, 04:25 PM #2
    dwsmith
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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 09:18 AM. Reason: Corrected per Mr. Fantastic's observation
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  3. December 10th 2010, 08:45 PM #3
    aukie
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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 07:50 AM.
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  4. December 11th 2010, 01:04 AM #4
    mr fantastic
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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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