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Limit at infinity

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data

    How can I prove that:

    [tex]\lim_{n \rightarrow \infty} n^{\frac{1}{n}}=1[/tex]

    Isn't [tex]\infty^{0}[/tex] indeterminate?
    Thanks!


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 20, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    Yes, it is indeterminant. That's not the end of the story. Indeterminant just means you don't know what the limit is yet. Take the log. Can you prove (1/n)*log(n) approaches 0?
     
  4. Oct 20, 2009 #3
    That becomes [tex]0*\infty[/tex], isn't that indeterminate as well?
     
  5. Oct 20, 2009 #4
    Can't you use L'Hopital's rule?
     
  6. Oct 20, 2009 #5
    Right. Thanks guys!
     
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