What a weird function.
I tried to find out: $\lim_{x\to\infty } \frac{\ln x}{\sqrt{x}\,{\sin{x}}}$
So, I can't use L'Hopital 'cause there's no actual limit in the denominator. It doesn't exist.
Then, I tried to use Heine's theorem and chose two sequences, but yet I got the same limit.
I believe it does not converge. How can I prove it?
Thanks