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Finding the limit of a function with e and ln

  1. Feb 22, 2005 #1
    lim as x->infinity [e^x + x] ^(1/x)

    Can anyone help me on this please, thanks.
     
  2. jcsd
  3. Feb 22, 2005 #2

    dextercioby

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    The limit is "e"...To convince yourself,use the fact that the limit & the natural logarithm commute.

    Daniel.
     
  4. Feb 22, 2005 #3
    can you take me one step further than that, to get the answer e?
     
  5. Feb 22, 2005 #4
    i got it now, thanks for the help
     
  6. Feb 22, 2005 #5

    dextercioby

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    There would be another way to do it,directly,without use of [itex] ln [/itex].Just factor e^{x} and then use the definition of "e":
    [tex] \lim_{u\rightarrow +\infty}(1+\frac{1}{u})^{u}=e [/tex]

    Daniel.
     
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