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oksanaekjord
 3 years ago
solve lim x>inf (ln x)^(1/x)
oksanaekjord
 3 years ago
solve lim x>inf (ln x)^(1/x)

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klimenkov
 3 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x\rightarrow\infty}(\ln x)^{\frac 1x}=1\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2start by taking the log get \[\frac{1}{x}\ln(\ln(x))=\frac{\ln(\ln(x))}{x}\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2now 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
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