I'm having trouble with this problem. Please help =)
Lim
X-> Infinity Ln(lnx) / x
I know if you plug infinity in there it'll be infinity over infinity and that's when you apply the L'H rule. But when I take the derivative for that it comes out to
X * 1/lnx * 1/x - Ln(lnX)
------------------------
X^2
which would equal -infinity / infinity right? But that's not the answer. The answer is 0 but i'm having trouble getting to it. any help will be appreciated. Thanks.
Thanks alot guys but I have another question on another problem. The problem is
X-> 1
Lnx / Sin(pi) X
The answer I got for this was -1 But my teacher got -1/pi. Here's my work
(1/x) / (sin pi + x * Cos pi)
If you plug 1 into all the X values you'll end up with 1 / -1 which equals -1 not -1/pi. Did I miss a step?