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Limit of x^((x^x)-1) as x->0

  1. Jan 26, 2013 #1
    1. The problem statement, all variables and given/known data
    Limit of x^((x^x)-1) as x->0


    2. Relevant equations
    Lim x^x=1
    x->0


    3. The attempt at a solution
    it's an 0^0 indetermination so I tried to solve it the usual way, by first calculating the limit of log(x)*(x^x-1) as x->0 with L'hopital's rule. I got e^0=1 confirmed by Wolfram. However, the using L'hopitals rule on this limit is not very practical, is there a better soluction?
     
  2. jcsd
  3. Jan 26, 2013 #2

    Zondrina

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    Suppose you let y = x^((x^x)-1), what is ln(y) = ?
     
  4. Jan 26, 2013 #3
    I would get the same limit log(x)*(x^x-1) as x->0 but solving this by L'hopital's rule takes a while or is it the fastest way?
     
  5. Jan 26, 2013 #4

    Zondrina

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    Oh whoops, I read too quickly. Yeah I don't see how you would do this without LH otherwise.
     
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