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

  • Thread starter tsuwal
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  • #1
tsuwal
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Homework Statement


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


Homework Equations


Lim x^x=1
x->0


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?
 

Answers and Replies

  • #2
STEMucator
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Suppose you let y = x^((x^x)-1), what is ln(y) = ?
 
  • #3
tsuwal
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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?
 
  • #4
STEMucator
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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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