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Limits question

  1. Oct 22, 2012 #1
    Hi, I'm having troubles wiith this problem:

    limit when x->∞ (1+2^x)^(1/x)


    I don't know how to proceed (I know I have to use l'Hospital's rule). It's a ∞^0 indetermination.


    Thanks!
     
  2. jcsd
  3. Oct 23, 2012 #2
    Try letting

    [itex]y=ln((1+2^{x})^{\frac{1}{x}})[/itex]

    Then what can you do??
     
    Last edited: Oct 23, 2012
  4. Oct 23, 2012 #3
    1/x goes down.
     
  5. Oct 23, 2012 #4
    now what form is it in? Can you use L'Hopitals rule now?
     
  6. Oct 23, 2012 #5
    Don't forget, that now

    [itex]e^{y}=(1+2^{x})^{\frac{1}{x}}[/itex]

    So when you find y, the limit of

    [itex]y=ln((1+2^{x})^{\frac{1}{x}})[/itex]

    you have to take [itex]e^{y}[/itex] to get the answer to the limit you're looking for.
     
  7. Oct 23, 2012 #6
    Ok I have:

    e^lim when x-> of ((ln(1-2^x)/x))

    L'Hôpital now?
     
    Last edited: Oct 23, 2012
  8. Oct 23, 2012 #7
    Well you should have

    lim x-->∞ [itex]\frac{ln(1+2^{x})}{x}[/itex]

    Then use L'Hopitals rule.

    You will find the limit of this. To get the answer you want you have to exponentiate it (since you took the natural log in order to find it).
     
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