# Thread: 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.

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

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 donīt have to differentiate the entire function, but the dividend and the divisor separately, thatīs what l'hopitalīs rule say.

If you donīt 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?

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

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

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

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

Hence the beauty of L'H rule!!