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An Implication of a limit rule

  1. Sep 13, 2012 #1
    1. The problem statement, all variables and given/known data

    If lim (x->∞) [ln(x^(1/x))]=0 and lim (x->∞) x^(1/x)=1, then does this

    =>

    lim (x->∞) [ln(x^(1/x))]= ln(lim(x->∞) [(x^(1/x))]) = ln(1)??

    2. Relevant equations

    lim (x->∞) [ln(x^(1/x))]=0 and lim (x->∞) x^(1/x)=1

    3. The attempt at a solution

    lim (x->∞) [ln(x^(1/x))]= ln(lim(x->∞) [(x^(1/x))] = ln(1)
     
  2. jcsd
  3. Sep 13, 2012 #2

    SammyS

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    Just what is the question?

    You do realize that ln(1) = 0, don't you ?
     
  4. Sep 13, 2012 #3
    Yes, but the question refers to the limit rules. This is what I am asking:


    lim (x->∞) [ln(x^(1/x))]= ln(lim(x->∞) [(x^(1/x))]) = ln(1)??

    To put it into words: Can the limit as x approaches infinity of [ln(x^(1/x))] be equal to the natural log of the limit as x approaches infinity of [(x^(1/x))] since lim (x->∞) [ln(x^(1/x))]=0 and lim (x->∞) x^(1/x)=1?
     
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