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sillybilly123:
Limits
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sillybilly123:
\(\lim\limits_{x \to \infty} x^{\frac{1}{\ln x}}\) Challenge Qu.
sillybilly123:
You can even use L'Hôpital, if you want
Vocaloid:
|dw:1513210240914:dw|
Vocaloid:
but in all seriousness, I believe you can take the natural log of the entire expression, bring the exponent down, cancel out the natural logs to get 1 making the actual limit e^1
Vocaloid:
I haven't taken calculus in 3+ years so I don't even remember why this works RIP
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sillybilly123:
Super smashing awesome !! \(\lim\limits_{x \to \infty}x ^{\frac{1}{\ln x}}\) \(= \lim\limits_{x \to \infty} \exp \left( ln (x ^{\frac{1}{\ln x}}) \right)\) \(= \lim\limits_{x \to \infty} \exp \left({\frac{1}{\ln x}} ln x \right) = e\)
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