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Math Help - L'Hopitals

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    L'Hopitals

    Find limit of (1+2x)^(1/(2lnx))
    as x approaches infinity...

    Could someone help me out? Thank You!
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  2. #2
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    Quote Originally Posted by Morgan82 View Post
    Find limit of (1+2x)^(1/(2lnx))
    as x approaches infinity...

    Could someone help me out? Thank You!
    let y = \lim_{x \to \infty} (1+2x)^{\frac{1}{2\ln{x}}}

    \ln{y} = \lim_{x \to \infty} \frac{\ln(1+2x)}{2\ln{x}}

    use L'Hopital ...

    \ln{y} = \lim_{x \to \infty} \frac{\frac{2}{1+2x}}{\frac{2}{x}}

    \ln{y} = \lim_{x \to \infty} \frac{x}{1+2x} = \frac{1}{2}

    y = e^{\frac{1}{2}} = \sqrt{e}
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