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oksanaekjord

  • 2 years ago

solve lim x->inf (ln x)^(1/x)

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  1. oksanaekjord
    • 2 years ago
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    getting 0

  2. klimenkov
    • 2 years ago
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    \[\lim_{x\rightarrow\infty}(\ln x)^{\frac 1x}=1\]

  3. satellite73
    • 2 years ago
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    start by taking the log get \[\frac{1}{x}\ln(\ln(x))=\frac{\ln(\ln(x))}{x}\]

  4. satellite73
    • 2 years ago
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    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

  5. oksanaekjord
    • 2 years ago
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    ty

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