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Thread: limit as x approaches 0 of xlog(x)

  1. #1
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    limit as x approaches 0 of xlog(x)

    \lim_{x \to 0}(xlogx)

    How do I go about rearranging xlogx in order to not have something undefined when I sub in x = 0? The only thing I can see to do is write it as:

    logx^x

    which is equally useless. I'm stuck on what to do with this one, any direction would be greatly appreciated.

    Is this the time to use L'Hospitals?

    Thanks.
    Last edited by terrorsquid; Nov 20th 2011 at 12:47 AM.
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  2. #2
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    Re: limit as x approaches 0 of xlog(x)

    Quote Originally Posted by terrorsquid View Post
    \lim_{x \to 0}(xlogx)

    How do I go about rearranging xlogx in order to not have something undefined when I sub in x = 0? The only thing I can see to do is write it as:

    logx^x

    which is equally useless. I'm stuck on what to do with this one, any direction would be greatly appreciated.

    Is this the time to use L'Hospitals? Yes. Write it as \color{red}\lim_{x\to0}\frac{\log x}{1/x} and use l'Hôpital.

    Thanks.
    ..
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