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Math Help - A Couple Limit Problems

  1. #1
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    Question A Couple Limit Problems

    1. lim x -> +infinity sqrt(9x^6 - x) / (x^3 + 1)

    2. lim x -> +infinity sqrt(9x^2 + x) - 3x

    Thanks a lot.
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  2. #2
    MHF Contributor red_dog's Avatar
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    1) \lim_{x\to\infty}\frac{\sqrt{9x^6-x}}{x^3+1}=\lim_{x\to\infty}\frac{x^3\sqrt{9-\frac{1}{x^5}}}{x^3\left(1+\frac{1}{x^3}\right)}=\  lim_{x\to\infty}\frac{\sqrt{9-\frac{1}{x^5}}}{1+\frac{1}{x^3}}=3

    2) \lim_{x\to\infty}(\sqrt{9x^2+x}-3x)=\lim_{x\to\infty}\frac{9x^2+x-9x^2}{\sqrt{9x^2+x}+3x}=\lim_{x\to\infty}\frac{x}{  x\left(\sqrt{9+\frac{1}{x}}+3\right)}=\frac{1}{6}
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  3. #3
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    Thanks for the help

    Can you please explain how you factored out x^3 in the denominator of the 1st problem?

    edit: never mind I see it now. Thanks a lot!
    Last edited by coolio; September 18th 2007 at 11:08 AM. Reason: nevermind
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