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Homework Help: Find the limit of

  1. Jan 31, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the limit of the following function

    lim w→∞ (1 + z/w)w

    2. Relevant equations



    3. The attempt at a solution

    lim w→∞ w ln(1 + z/w)

    Not sure where to go next...

    Thanks
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 31, 2012 #2
    I've tried l'Hopitals rule, but I don't think I'm any closer.
     
  4. Jan 31, 2012 #3
    Can you show how you tried l'Hopital's rule? Because I tried it and it worked.
     
  5. Jan 31, 2012 #4
    w/(1 + z/w) + 1/ln(1 +z/w)
     
  6. Jan 31, 2012 #5
    I think I may have forgot the chain rule...
     
  7. Jan 31, 2012 #6

    Dick

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    w ln(1 + z/w) has the form infinity*0. You'll want to arrange it into an infinity/infinity form before you do l'Hopital. Can you show how you tried to apply it?
     
  8. Jan 31, 2012 #7
    lim w→∞ w.ln(1/w*(w+z))
     
  9. Jan 31, 2012 #8
    After l'Hopital I'm getting lim w → ∞ ( -z/(w+z) + ln(1 + z/w))

    This doesn't seem to help, not unless I'm doing something stupid.
     
  10. Jan 31, 2012 #9

    Dick

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    That's still infinity*0. Try rearranging it into [itex]\frac{ln(1+\frac{z}{w})}{\frac{1}{w}}[/itex]. That's 0/0.
     
  11. Jan 31, 2012 #10
    I've done that, but it still brings me to this.
     
  12. Jan 31, 2012 #11
    Wait, the penny dropped. The answer is z. You multiply across by -(w+z) :) Thanks for all your help.!!
     
  13. Jan 31, 2012 #12
    ... not forgetting you took the logarithm at the start.
     
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