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Math Help - Quick limit help.

  1. #1
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    Quick limit help.

    Hi, im trying to find the limit of xln(x) as it approaches 0+. I think the limit of ln(x) is undefined making it infinite right? But would the x at the begining make the limit approach 0?
    Thank you.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by cowboys111 View Post
    Hi, im trying to find the limit of xln(x) as it approaches 0+. I think the limit of ln(x) is undefined making it infinite right? But would the x at the begining make the limit approach 0?
    Thank you.
    Note that \lim_{x\to{0^+}}x\ln x=\lim_{x\to{0^+}}\frac{\ln x}{\frac{1}{x}}

    you have the indeterminate case \frac{\infty}{\infty}.

    We can now apply L'Hopital's rule:

    \therefore\lim_{x\to{0^+}}\frac{\ln x}{\frac{1}{x}}=\lim_{x\to{0^+}}\frac{\frac{1}{x}}  {-\frac{1}{x^2}}=\lim_{x\to{0^+}}-\frac{1}{\frac{1}{x}}=\lim_{x\to{0^+}}-x=\color{red}\boxed{0}

    Does this make sense?

    --Chris
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  3. #3
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    Yes it does, thank you.
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