Question

Limits

Answer 1

\(\lim\limits_{x \to \infty} x^{\frac{1}{\ln x}}\)

Challenge Qu.

Answer 2

You can even use L'Hôpital, if you want

Answer 3

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

Answer 4

I haven't taken calculus in 3+ years so I don't even remember why this works RIP

Answer 5

Super smashing awesome !!

\(\lim\limits_{x \to \infty}x ^{\frac{1}{\ln x}}\)

\(= \lim\limits_{x \to \infty} \exp \left( ln (x ^{\frac{1}{\ln x}}) \right)\)

\(= \lim\limits_{x \to \infty} \exp \left({\frac{1}{\ln x}} ln x \right) = e\)