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.