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Homework Help: Estimates of the natural log

  1. Apr 25, 2010 #1
    1. The problem statement, all variables and given/known data

    using the following definition: ln x = [tex]\int dx/x[/tex], give best possible upper and lower estimates of ln n, n a positive integer.

    then, use this result to show that the limit of the function as n approaches infinity is infinity.

    2. Relevant equations

    3. The attempt at a solution
    Unfortunately I have no idea what to attempt -- I don't know how to find estimates, and I'm not really sure what that means -- this is for a history of math class so I have no textbook context to look though either. Any explanations/tips would be very helpful, thanks!
  2. jcsd
  3. Apr 25, 2010 #2


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    Science Advisor
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    Gold Member

    You probably mean to define

    [tex]\ln{(x)} = \int_1^x\, \frac 1 t\, dt[/tex]

    Try looking at upper and lower rectangular approximating sums.
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