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".
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.
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').
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.
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
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.
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.
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.
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".
good.
In the definition of limit the neighborhood must be a perforated neighborhood so it is 0
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.
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
I love your username
the best subscriber
Good place to start at 0:00
5:40 notice that t could also be equal to b, where function is not necessarily defined either
Heckin good video
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?
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.
@@DeanCalhoun Yeah you're right, it has to be an indeterminate form to be interesting. Thank you!
Gotta love real analysis
ooh, time for a more rigorous refresher on everything that was brushed under the rug in AP calc
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
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?
I think you're right, everything seems to work without these two being equal to eachother.
what is happening if g(x) approach negative inf, because I cannot yet understand what will happen in this case
Good
Did you mean: L'Hôpital's
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.
he did the 0/0 case in the last video, it's indeed way easier
@@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
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.
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.
I dislike L'Hospital' theorem cause they did Bernoulli's bad even with taylor
Spooky ghost goth girl on the blackboard :o