Originally posted by TheGeneral
He is right you know, the Hospital\'s guy rule works for any form of 1/0 or 0/1, but not infinity/infinity, I dun think. Don\'t quote me on this.
Hum, I quote you nevertheless
What I meant is that it applies to both infinity/infinity and 0/0 (it\'s only a view of the mind, both are the same) for functions that are continuous around
a . That\'s precisely the point of this theorem, otherwise it wouldn\'t be possible to compute the limit so easily.
If I remember well, because it\'s more than 10 years away
(btw 1/0 tends to infinity and 0/1 to 0, those are trivial cases)
Originally posted by lynx_lupo
I\'ve never heard of that rule, but the way I see it, the first limit(?) is 1 and the second limit\'s parameters are just diferentials, so the functions are pretty much the same. Especially near infinity. Because for first to be one, a=infinity or the functions are very quickly rising(like exponential). So, the second one is also 1, which is 1.
No, you can\'t say the limit of infinity/infinity is 1. For instance (bad example but I lack the time atm), 2/x and 4/x are both tending to infinity when x tends to 0. I don\'t get your point for the rest (?).
To see how the H?pital\'s theorem can be useful, take f(x)=1/x and g(x)=ln(x^2), you\'ll see it\'s worth it.
