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Math Help - limits to infinity

  1. #1
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    limits to infinity

    how do you find the lim ((x^2+ 4x+3)^(1/2) -x) as x tends to infinity?

    as well as lim ((x^2 +1 )^(1/2) / x) as x tends to negative infinity?

    thanks you
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    how do you find the lim ((x^2+ 4x+3)^(1/2) -x) as x tends to infinity?

    as well as lim ((x^2 +1 )^(1/2) / x) as x tends to negative infinity?

    thanks you
    This is the trick you're looking for:

    \lim_{x->\infty}\sqrt{x^2+4x+3}-x=\lim_{x->\infty}(\sqrt{x^2+4x+3}-x)\frac{\sqrt{x^2+4x+3}+x}{\sqrt{x^2+4x+3}+x}

    Do you know how to procede from here? This is just the standard method for dealing with infinite limits of functions like this.
    Last edited by adkinsjr; November 14th 2009 at 05:51 PM.
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