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Math Help - How to solve this limit

  1. #1
    Junior Member
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    How to solve this limit

    Hey,
    I'm having a hard time trying to solve both of these limits :
    1.lim(sqrt(x^2 +x) -x) = 0.5
    x->inf

    2.lim(sqrt(x^2 +x) -x) != 0.5 (Not equal)
    x->-inf

    I would be glad if someone could post an epsilon-delta (Or other way) solution to these limits
    Thanks a lot !
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  2. #2
    MHF Contributor

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    Re: How to solve this limit

    Quote Originally Posted by MichaelEngstler View Post
    Hey,
    I'm having a hard time trying to solve both of these limits :
    1.lim(sqrt(x^2 +x) -x) = 0.5
    x->inf

    2.lim(sqrt{x^2 +x} -x) != 0.5 (Not equal)
    x->-inf
    \sqrt{x^2+x}-x=\frac{x}{\sqrt{x^2+x}+x} now divide through by |x|.
    Last edited by Plato; October 25th 2012 at 02:32 PM.
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