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Thread: Limits

  1. #1
    mei
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    Limits

    Hey!

    I'm not quite sure how to proceed in calculating this limit.
    If you could look at it and give me some feedback I would appreciate it.

    \lim_{x \to +\infty} \frac{xln(e^x+e^{-x})+\sqrt{x^3+1}}{x^2+1}

    Thanks in advance.
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  2. #2
    Super Member malaygoel's Avatar
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    these might help you

    xln(e^x+e^{-x})

    = x[ln(1+e^{-2x})+x]
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  3. #3
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    After using that, divide both numerator and denominator by x^2.
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  4. #4
    mei
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    Thank you!
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  5. #5
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    Here's a hand-waving argument, for large x

     <br />
\frac{x \ln(e^x+e^{-x})+\sqrt{x^3+1}}{x^2+1} \approx \frac{x \ln(e^x)}{x^2} = \frac{x^2}{x^2} = 1
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  6. #6
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by mei View Post
    Hey!

    I'm not quite sure how to proceed in calculating this limit.
    If you could look at it and give me some feedback I would appreciate it.

    \lim_{x \to +\infty} \frac{xln(e^x+e^{-x})+\sqrt{x^3+1}}{x^2+1}

    Thanks in advance.
    You can divide all three terms by x^2

    and concentrate on {\ln(e^x+e^{-x})\over x}
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