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Math Help - Limits - Degree Level Analysis

  1. #1
    Newbie
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    Jan 2009
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    Limits - Degree Level Analysis

    Hi,
    I'm trying to prove that 2n/(n^3+1) is a null sequence. I have done the modulus of this < epsilon.

    Ended up with 2n < E(n^3+1)

    Where do I go from here? I can't work out how to simplify it
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  2. #2
    Senior Member
    Joined
    Nov 2007
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    \frac {2n}{n^3+1}=\frac {\frac 2{n^2}}{1+\frac 1{n^3}}
    We know that (if you don't then you should try to prove it) \lim_{n\rightarrow\infty}\frac 2{n^2}=0 and \lim_{n\rightarrow\infty}\frac 1{n^3}=0 therefore \lim_{n\rightarrow\infty}\frac {\frac 2{n^2}}{1+\frac 1{n^3}}=\frac 01=0.
    Last edited by james_bond; January 14th 2009 at 07:46 AM.
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