l'hospital's rule?

Question

can i apply l'hospital's rule to negative infinity minus infinty? ex. lim f(x)-g(x)= -(inf)-(inf)
put this one on already, but need more info

why bother, this is too much for you meatheads

Answer 1

L'Hospital's rule only applies to the ratio of two functions, so it doesn't apply directly to this difference. A trick you might try is to exponentiate the difference. Or by observing that:

f(x) - g(x) = ln [ exp(f(x)) / exp(g(x)) ].

You can apply the rule to the ratio [ exp(f(x)) / exp(g(x)) ], which gives that its limit as x→∞ is equal to:

lim = [ exp(f(x)) (df(x)/dx) ] / [exp(g(x)) (dg(x)/dx)].
x→∞

If you can evaluate that limit, take the ln() (natural log) of the result and you have the limit you're after.

Of course, if f(x) and g(x) have finite limits then you don't need L'Hospital's rule, but you wouldn't be asking about it if that were the case.

Answer 2

Well, then, rather than ask us meatheads, I might suggest you do your own research. Here's a Web site you can start with:

http://mathworld.wolfram.com/LHospitalsRule.html

By the way, my meathead interpretation of this is that it applies only to division, not subtraction (as the first meathead said).

Answer 3

If you need more information, you need to put more information too :P, but the answer is no, you can't use l'hopital for such indeterminate form.

Answer 4

the rule is for (a(x)/b(x)) not a subtraction