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Limit of this at infinity?

  1. Apr 11, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex]\lim x-> \infty [x+1-ln(x+1)][/tex]

    2. Relevant equations

    3. The attempt at a solution
    How does one evaluate this? I don't know how to use L'Hopital's rule on this and I have infinity- infinity, which is indeterminate. Thanks!
  2. jcsd
  3. Apr 11, 2008 #2


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    There is a fairly standard technique for going from "a-b" that leads to "[itex]\infty[/itex]- [itex]\infty[/itex]" to a "0/0" or "[itex]\infty/\infty[/itex]", given in every Calculus text I know: multiply both numerator and denominator by the "conjuate" a+ b. In this case that gives
    [tex]\frac{(x+1)^2- (ln(x+1))^2}{x+1+ ln(x+1)}[/tex]
    That is now of the form "[itex]\infty/\infty[/itex]" and you can use L'Hopital's rule.
  4. Apr 11, 2008 #3
    Ok thanks.
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