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Calculate the limit

  1. Apr 24, 2009 #1
    1. The problem statement, all variables and given/known data

    3/ (x (ln (x+4) - ln (x))

    as x goes to infinity.

    so first i look at this i i thought its going to 0 cause x is gonna get larger at the bottom.

    but then i see that the equation looks more like 3 / (x( ln ((x+1)/x))
    ln ((x+1)/x) is going to 1. so that mean that ln 1= 0

    so...
    3 / x(0) = infinty???
     
  2. jcsd
  3. Apr 24, 2009 #2

    dx

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    Nope, not infinity.

    Hint: ln(a) - ln(b) = ln(a/b) and (1 + a/x)x → ea as x → ∞
     
  4. Apr 24, 2009 #3
    it doesnt go to zero?
     
  5. Apr 25, 2009 #4

    dx

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    No. The limit is a positive number.
     
    Last edited: Apr 25, 2009
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