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Limit question (inf. - inf.)

  1. Feb 8, 2005 #1


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    Hello all,

    I have this problem I can't solve.. it is a infinite - infinite. I tried it around 5 times and can't find the correct answer (infinite). I'm pretty sure I have to put in evidence x^2 and use a limit law but I can't find the answer.. can someone help me for this problem:

    lim x -> +inf. [tex] x - \ln(x^2-1) [/tex]

    Thanks very much in advance.
    Last edited: Feb 8, 2005
  2. jcsd
  3. Feb 8, 2005 #2
    The limit evaluates to -0.5? How do you know this?

  4. Feb 8, 2005 #3


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    That's the answer in the book =)

    Sorry, it was x - (lnx^2-1)
    Last edited: Feb 8, 2005
  5. Feb 8, 2005 #4
    x^2 increases much faster than ln(x^2 -1). The limit should be unbounded.

    The technique I'd use to evaluate it would be to write x^2 as [itex]\ln{\left(e^{x^2}\right)}[/tex] and then combine the logs. This approach gives a result of infinity, as well.

  6. Feb 8, 2005 #5


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    I edited the equation. It was a typo.. sorry
  7. Feb 8, 2005 #6
    [tex]x - \left(\ln{x^2}\right) - 1[/tex]
    [tex]x - \ln{(x^2 -1)}[/tex]

    Well, either way, the limit is still unbounded.

  8. Feb 8, 2005 #7


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    This one. I will try your method. Is it the only way?
  9. Feb 8, 2005 #8
    Heh, I screwed up the notation, too. I edited to give the proper two possibilities. As it was before, they said exactly the same thing!

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