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Homework Help: Lim n[tex]\rightarrow[/tex][tex]\infty[/tex] (1+(x/n))[tex]^{n}[/tex]

  1. Oct 25, 2008 #1
    lim n[tex]\rightarrow[/tex][tex]\infty[/tex] (1+(x/n))[tex]^{n}[/tex]

    I have no idea where to start. Can anyone who knows what to do give me a hint or tell me the first step? Thanks
     
  2. jcsd
  3. Oct 25, 2008 #2

    HallsofIvy

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    That looks an awful lot like an exponential function to me. Take the logarithm of [itex](1+(x/n))^n[/itex] and you have a limit, as n goes to infinity, of the form [itex]0*\infty[/itex]. That can be rewritten as so that it is of the form "0/0" and, even though here n is an integer, you can use L'Hopital's rule.
     
    Last edited by a moderator: Oct 26, 2008
  4. Oct 26, 2008 #3
    I'm pretty sure I can't pull the one out of the parenthesis like that. Like when you foil you always have a middle term? So with this we should have n+1 terms, but if we take the one out it chages the equation and we only have two terms if we expand it
     
  5. Oct 26, 2008 #4
    Maybe I'm wrong. If I can't come up with something better I will do that
     
  6. Oct 26, 2008 #5

    HallsofIvy

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    The 1 was supposed to be in the parentheses! I have edited my previous post.

    The logarithm of [itex](1+ (x/n))^n[/itex] is n log(1+ (x/n)) which, as I said, is of the form "[itex]0*\infty[/itex]". You can write that as log(1+ (x/n))/(1/n) so that it is now of the form "0/0". Apply L'Hopital's rule treating the n as a continuous variable.
     
  7. Oct 26, 2008 #6
    alright. thanks so much!
     
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