1. Apr 24, 2009 #1

   intenzxboi

   

   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???

    

   intenzxboi, Apr 24, 2009
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3. Apr 24, 2009 #2

   dx

   

   Homework Helper

   Gold Member

   Nope, not infinity.
   
   Hint: ln(a) - ln(b) = ln(a/b) and (1 + a/x)^x → e^a as x → ∞

    

   dx, Apr 24, 2009
4. Apr 24, 2009 #3

   intenzxboi

   

   it doesnt go to zero?

    

   intenzxboi, Apr 24, 2009
5. Apr 25, 2009 #4

   dx

   

   Homework Helper

   Gold Member

   No. The limit is a positive number.

    

   Last edited: Apr 25, 2009

   dx, Apr 25, 2009

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