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Homework Help: L'Hopital's rule of x*ln(x)-x

  1. Mar 17, 2009 #1
    1. The problem statement, all variables and given/known data
    What is the value of xln(x)-x when x=0?

    2. Relevant equations
    I'm assuming you do L'Hopital's

    3. The attempt at a solution
    I'm assuming you factor out the x, leaving:


    but that's still not in the form of [tex]\frac{\infty}{\infty}[/tex] or [tex]\frac{0}{0}[/tex]

    Would you do:




  2. jcsd
  3. Mar 17, 2009 #2


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    Homework Helper
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    [tex]\lim_{x\to 0} x\ln(x)-x=(\lim_{x\to 0} x\ln(x))-(\lim_{x\to 0} x)[/tex] :wink:
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