Real Analysis | L'Hospital's Rule (∞/∞ - case)
We carefully prove the infinity / infinity case of L'Hospital's rule for calculating limits of indeterminate forms.
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Пікірлер: 31
I got maybe 7 minutes in, and this reminds me how I managed by some miracle to get through my freshman calculus year. Today I need strong coffee for this 20 minute video.
Hi, For fun: 3 "let's go ahead and", 1 "let's just go ahead and point out", 1 "now we want to go ahead and", 1 "I'll may be go ahead and", 1 "may be I'll go ahead and", 1 "the next thing that I want to notice", 2 "the next thing that I want to do", 1 "the important thing that I want to notice here", 2 "great".
@rayniac211
3 жыл бұрын
good.
In the definition of limit the neighborhood must be a perforated neighborhood so it is 0
It may be useful to know that, when the denominator tends to ±∞, the de l'Hôpital rule always holds, no matter what the numerator tends to. Of course, it may not be an indeterminate form, but still lim (f/g) = lim (f'/g').
Is he actually teaching a class with these videos and some of us are just weirdos tuning in for fun?
20:10
@thedoublehelix5661
3 жыл бұрын
I love your username
@stenarsk6877
3 жыл бұрын
the best subscriber
@goodplacetostart9099
3 жыл бұрын
Good place to start at 0:00
Heckin good video
5:40 notice that t could also be equal to b, where function is not necessarily defined either
Thank you so much for this great explanation 👍
What a cool video. But when did you use the fact that the limit of f is tending to infinity?
@DeanCalhoun
3 жыл бұрын
From what I gather, the only strict requirement is that g tend towards infinity. But if f doesn’t also tend towards infinity, then the limit will simply be zero and the theorem is unnecessary.
@TheMauror22
3 жыл бұрын
@@DeanCalhoun Yeah you're right, it has to be an indeterminate form to be interesting. Thank you!
11:38 Im trying to prove the second case where the limit of g(x) is negative infinity and I have a question. So we can change the proof to say that there is a delta2>0 such that 0
Gotta love real analysis
ooh, time for a more rigorous refresher on everything that was brushed under the rug in AP calc
what is happening if g(x) approach negative inf, because I cannot yet understand what will happen in this case
Hi Michael, I think g(x) should greater than g(t) on 10:41. If g(x) is greater than or equal to g(t), it would be disastrous. What do you think?
@Nusret15220
11 ай бұрын
I think you're right, everything seems to work without these two being equal to eachother.
Good
Did you mean: L'Hôpital's
Spooky ghost goth girl on the blackboard :o
I dislike L'Hospital' theorem cause they did Bernoulli's bad even with taylor
This seems harder than I remember. Maybe I'm misremembering, but I thought this proof was easier if you assume f(x)->0 and g(x)->0 instead of infinity.
@okra_
3 жыл бұрын
he did the 0/0 case in the last video, it's indeed way easier
@JM-us3fr
3 жыл бұрын
@@okra_ Oh okay. Then can't he prove this case by noting f(x)/g(x) is the same as (1/g(x))/(1/f(x))? Then just apply the 0/0 case
@SlimThrull
3 жыл бұрын
I think the proof presented here is much more in depth than most people get when they first learn L'Hospital's Rule. I recall my professor sort of glossing over a lot of this and then "magically" coming up with how it all works out in the end.
@stephenbeck7222
3 жыл бұрын
SlimThrull well this is for an analysis course. The method of proof is much more important than the results, which is the opposite of a first year calculus class where most encounter this rule.