L'Hopital's Rule for Solving Indeterminate Form (-∞)/∞

[kasse]

Can one use L'Hopital's Rule on the indeterminate form (-∞)/∞ ?

And by the way, is there a way to write mathematical signs like ∞, the integral sign etc except google-ing, cutting and pasting?

 

[courtrigrad]

I think you can. It would probably be:

$$-\lim_{x\rightarrow c} \frac{f(x)}{g(x)}$$ so that both functions approach $$\infty$$

you write those signs in $$tags as follows: \infty \int$$

 

[kasse]

Yes, it's a french name. But that doesn't really help me a lot

 

[kasse]

OK, thanks!

 

[Tomsk]

I'm not sure, I think its only 0/0, as it comes from the Taylor expansion about the point that x approaches, ie.

$$\lim_{x\rightarrow a}\frac{f(x)}{g(x)} = \lim_{x\rightarrow a}\frac{f(a) + f'(x)(x-a) + ...}{g(a) + g'(x)(x-a) + ...} = \lim_{x\rightarrow a}\frac{f'(x)}{g'(x)}$$

With f(a)=g(a)=0

Something like that anyway.

 

[courtrigrad]

No you can use l'hospital's Rule for indeterminate forms, not just 0/0.