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Math Help - Finding the limit for x->∞

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    Finding the limit for x->∞

    How do I find the limit of

    (root(9x^2 + x)) - 3x when x -> ∞?
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by sweetadam View Post
    How do I find the limit of

    (root(9x^2 + x)) - 3x when x -> ∞?
    \lim_{x\to\infty}\sqrt{9x^2+x}-3x

    = \lim_{x\to\infty}(\sqrt{9x^2+x}-3x)\frac{\sqrt{9x^2+x}+3x}{\sqrt{9x^2+x}+3x}

    = \lim_{x\to\infty}\frac{x}{\sqrt{9x^2+x}+3x}

    = \lim_{x\to\infty}\frac{1}{\sqrt{9+\frac{1}{x}}+3}

    = \frac{1}{\sqrt{9+0}+3}

    = \frac{1}{6}
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