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I need help solving a limit

  1. Jun 11, 2009 #1
    1. The problem statement, all variables and given/known data

    The problem is

    Limit [x.log(x)]

    2. Relevant equations

    Consider Log being a logarithm of base 10

    This will tend to +oo, but x.log(x) will become (oo).(oo) wich is an indetermination I need to know how to solve the indetermination in this case

    3. The attempt at a solution

    Thanks for all help
  2. jcsd
  3. Jun 11, 2009 #2


    Staff: Mentor

    [itex]\infty * \infty[/itex] is NOT an indeterminate form. If you have two quantities that are getting larger and larger, their product will, too. The limit is infinity.
  4. Jun 12, 2009 #3
    Bear in mind that
    [tex] x\log(x) = \frac{\log(x)}{\frac{1}{x}}.[/tex]
    Given that form, you can apply l'Hopital's rule.
  5. Jun 12, 2009 #4


    User Avatar
    Science Advisor

    No, you can't. That becomes "infinity over 0" which, again, is NOT an "indeterminant". L'Hopilal's rule does not apply and you don't need it.
  6. Jun 12, 2009 #5
    My apologies; read it too quickly and thought we were talking about a limit as x->0+.
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