anonymous
  • anonymous
solve lim x->inf (ln x)^(1/x)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
getting 0
klimenkov
  • klimenkov
\[\lim_{x\rightarrow\infty}(\ln x)^{\frac 1x}=1\]
anonymous
  • anonymous
start by taking the log get \[\frac{1}{x}\ln(\ln(x))=\frac{\ln(\ln(x))}{x}\]

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anonymous
  • anonymous
now that limit is pretty clearly 0, since log grows much slower than \(x\) and the log of the log grows amazingly slowly since that limit is 0, and it is the limit of the log, you get \(e^0=1\) and the limit of your original question
anonymous
  • anonymous
ty

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