# Math Help - L'Hopitals Rule

1. ## L'Hopitals Rule

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.

2. Originally Posted by Afterme

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.

For L'H rule you dont use the quotient rule.

$\lim_{x \to \infty}\frac{f(x)}{g(x)}=\lim_{x \to \infty}\frac{f'(x)}{g'(x)}$

Take the deriavative of the numerator, then the derivative on the denominator and then take their limits

3. OMG Thanks alot =)!! I forgot about that little rule haha. THANK YOU VERY MUCHHHHHH!!!

4. You don´t have to differentiate the entire function, but the dividend and the divisor separately, that´s what l'hopital´s rule say.

If you don´t get the right result tell me and I write it down for you; happens that I suck with latex...

5. 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?

6. do you know the chain rule?

$\frac{d}{dx} \sin(\pi x) = \pi \cos(\pi x)$

7. Originally Posted by TheEmptySet
For L'H rule you dont use the quotient rule.

$\lim_{x \to \infty}\frac{f(x)}{g(x)}=\lim_{x \to \infty}\frac{f'(x)}{g'(x)}$

Take the deriavative of the numerator, then the derivative on the denominator and then take their limits

Hence the beauty of L'H rule!!