Learned about this rule in my Ap Calc AB class a few months ago. I asked the teacher where it came from and why it works and she said to just use it and she didn’t fully know. Thanks for teaching me! I find calculus very fascinating to learn and it’s people like you who make the world a better place. Consider becoming a teacher, you are very skilled!

most intuitive explaining I've ever seen 😲

@serhatcoban6797

4 жыл бұрын

Then, you dont know 3 blue 1 brown😁

@mousaalsaeed9410

4 жыл бұрын

@@serhatcoban6797 That's a long time ago

@serhatcoban6797

4 жыл бұрын

@@mousaalsaeed9410 😂

@greenhat7618

3 жыл бұрын

@@serhatcoban6797 maybe I’m dumb but I find this explanation on lhopital more intuitive than the 3b1b vid. Ofc his vids are great i loved his vid on taylor series.

What a great explanation! Sometimes a graphical demonstration like this, although not a rigorous proof to the academic standard, is sufficient for the student to "see" why some rule works. I had a similar problem when shown Descartes' Rule of Signs, but with no proof offered. When I tried to find a proof of Descartes' Rule, the offerings were too advanced for me. Eventually, I reasoned out a graphical justification for Descartes' Rule myself, and that was sufficient to put me "at peace" with the rule and move on.

This was an excellent intuitive proof! It was carefully explained and easy to understand. So worth the time to watch! Also, your handwriting is very clean and neat!

@Snillocad143

3 жыл бұрын

I think that the word "intuitive" is an error of application. You are providing a proof explicitly which looks more to have come from first principles and which is an axiomatic reproduction of what l'Hopital would have used himself. Your explanation is clear but there is no circuitous other argument which would avoid obfuscation. For example, for me an intuitive argument would appear to explain l'Hopital's rule without the ideas what you have shown here and thereby move almost to claim credit for the result. Not only would that be a fanciful doubletalk, namely bullshit, but I can't think of how one could connect such disconnected ideas to what we know as an elegant and simple rule.

I loved this! Certainly one of the better KZreadrs I’ve seen in terms of ability to explain and not leave holes for the student

Beautiful! Thanks for taking the time to produce this video, everything is now Chrystal clear!

I figured this proof out on my own - and I didn't even remember that it was actually L'Hopital's rule!

@derekowens

5 жыл бұрын

Excellent! You are thinking the same thoughts as some of the greatest mathematicians!

I really like how you graphed each function independently! That is super helpful and offers a new ways to use L'Hopital's Rule

This was an unbelievably helpful and clearly explained video, thank you Derek!

You know when you know why something is the case, but you can't really explain it, and then someone does it for you so elegantly that your own understanding improves? That's this video. Thanks.

Congratulations for the video. Great work!

Fantastic. I am sharing this with all my students from now on. Thanks.

Fantastic graph and method of explanation. This should be put into all textbooks

What a fantastic explanation. Thank you very, very, much.

This was beautiful! Thank you. You just got a new subscriber buddy!

Beautiful. Exactly the kind of proof I was looking for.

Thanks for the intuitive explanation

EXCELLENT explanation, thanks!

Bro you just got that done! Excellent!

Just wonderful! Many thanks.

Excellent explanation yet so simple to understand!

Excellent explanation. Thank you!

i am starting to understand what df/dx means in my calc 1 class. It really helps visualize what i am solving for instead of just plugging in numbers and getting the answer. I feel closer to math every time i see a good explanation of a concept.

@xxMpEGxx

Жыл бұрын

you are calculating an infinitesimal difference in height divided by an infinitesimal difference in width = slope same goes for Integrals: that big integral sign stands for Summation and the term f(x) inside is the height times the infinitesimally small width dx which results in the infinitesimal area, which is then summed up for each infinitesimally small dx over the interval

@quest4knowledge-xh3eu

4 ай бұрын

the good news is that dx and dy , df etc are NOT infinitesimals. But that's a new discovery. Seek and you shall find.

Wonderful proof dereck. you may want to use Desmos to do your graphing in the future though, it looks a lot neater than the emulated calculator :D

Hey, I finally understand Lhopital's rule! This tutorial rocks

Starting this video: "how the hell does l'hospital actually work?" Exiting: "yeah, that makes sense." Thanks🎉

Very smart explanation, thank you!

Of all the explainations that i saw,it was the best

omg this is the only tutorial that showed why assumption of f(a) = 0 is a valid assumption, thank you!

@derekowens

4 жыл бұрын

You get it, man! The function has to equal zero at that point or it's not valid.

Thanks you help me clear my doubts.

Bless you Derek Owens

WOW great intuitive video!!!

Intuitive and awesome!!!

Wonderful, but could you please provide me with more explanation for the case of infinite/infinite? It sounds like limit f(x)/g(x) = limit (1/g(x))/(1/f(x))=d(1/g(x))/d(1/f(x)), which is not equal to df(x)/dg(x)

@amiyancandol4499

3 жыл бұрын

After that (g'/f')(f²/g²)=f/g , so 2possibilities, either f/g=0 or f'/g'=f/g so there's that

Brilliant video!

That's the best L'H♡SPITAL video.Even KHAN ACADEMY CAN'T beat IT.

@KarenWasherGrudzien

3 жыл бұрын

Yes, except for the very unnecessary part where he refers to some sort of "curvature"in the earth that does not exist in our reality. The earth is flat, we aint no globe!!!

@AhmedMahmoud-tv9vw

3 жыл бұрын

@@KarenWasherGrudzien OK Karen

@KarenWasherGrudzien

3 жыл бұрын

OK Muhammad

@mathlegendno12

3 жыл бұрын

@@KarenWasherGrudzien Were you joking

@KarenWasherGrudzien

3 жыл бұрын

@@mathlegendno12 No

Great video, hope you get more views :)

Excellent video! 10/10

Great video!

Awsome! Thanks so much!!

it's awesome. thank you.

Smart thinking. Never really looked at it this way :D

beautiful...plain beautiful

So technically earth is indeed flat if you zoom in by a lot

@derekowens

3 жыл бұрын

Exactly! If you ignore the terrain. The earth is curved, but locally it is flat. And if it's not flat enough for you, just move in closer and zoom in a little more.

Very very helpful 😍😍 thank you

ONE OF THE MOST FAVOUR MY THEOREM OF CALCULUS ................

Amazing!

what an amazing video .. love it :) can you please tell me what software you use to create these videos? thanks

Excellent

this was so good....

Well explained

Thank you

thank you kind sir

You are amazing

amazing 👌😍😍

good explanation

you could also explain it as: if you find the derivative of f and the derivative of g using the definition of the derivative, then you divide them, you will be left with f(a+h)/g(a+h) where 'a' is the value that x is approaching and h is approaching 0. So essentially you are dividing a point on f thats infinitely close to 'a', by a point on g thats infinitely close to 'a'

I'm someone who has dyscalculia and honestly it blows my mind when this makes sense to me more than simple Maths???

@loopingdope

7 жыл бұрын

What is dyscalculia? Similiar to dyslexia but with math and numbers?

@miacapaldi822

7 жыл бұрын

loopingdope yeah pretty much. reading numbers is difficult, as well as counting, remembering facts, misunderstanding place value and anxiety surrounding the subject itself. It's really difficult

@loopingdope

7 жыл бұрын

You can understand maths from videos like these ones? And this is a rather "hard" subject compared to regular math. It's kind of strange, but best of luck to you and I hope that you'll end up fine.

@jitendra_9973

5 жыл бұрын

I'm an UG B.tech 1st year student. I've already realized this proof during studying the Thomas's calculus book. And many other proofs like this also have I realized by myself. I think I am a different. What is the best thing I should do ? Because I am confused what I should do. Can you tell me what is best for me ? (Currently I am an electrical engineering UG student) All my classmates are blindly learning coding just to get good job in companies like Google. Please help me !!!

@johnhugon67

5 жыл бұрын

@@jitendra_9973 "All my classmates are blindly learning coding" Listening to what a random person on the internet tells you to isn't the way to figure out what to do for the rest of your life and is just as blind as what you criticize your classmates for. Understanding a proof like this doesn't make you special in any way either. Do what you enjoy, and if there's nothing you enjoy noticeably more than other subjects, pick something you would be able to tolerate for a long time and pays decently (nothing you couldnt imagine yourself doing for 20yrs or longer). You can search for your passion while you work at a well paying job, but make sure you don't attempt to make anything you dislike your career, you'll hate your life.

thanks

بحسها بتحكي عني انا واختي واخويا بعيد عننا 😭😭 انا شاء الله سيجمع شملنا ❤

My understanding of this is that limx-->c f(x)/g(x), is "rise_f over rise_g". While the ratio of derivatives is " (rise_f/run)/(rise_g/run) = rise_f over rise_g".

3blue1brown style of intuitive demonstration

cool

What if x -> infinity ? How would this type of graphical proof look like ? I ask this because I've tried every which way and i find it impossible ( my case is a 0/0 case as x -> ∞ where f(x)=1/(4x^2 -5x) and g(x)=1/(1-3x^2) ). Thank you for the video!

@DoofEvil

8 ай бұрын

be explains it in the end, where he shows how ♾️/♾️ = 0/0

@Derek Owens What I've learned from this video: zero/zero = infinity/infinity Just kidding amazing video which gave me a lot of insight Now you've just made me interested in the relationship I mentioned above I don't feel like the mathematical community is very comfortable with it

@kanerashiki1046

5 жыл бұрын

Nor that I can learn much about it from existing resources

@cpotisch

4 жыл бұрын

They’re both indeterminate forms, but they can’t really be equated.

PROBLEM WE DON'T HAVE TIME TO DERIVE FORMULA WHEN YOU DO THE EXAMS ........... THE EXAM QUESTION ONLY GIVE YOU ENOUGH TIME TO SOLVE EACH PROBLEM ............... LIMIT TIME FOR EACH QUESTION ................ IF YOU ARE LATE FOR ONE QUESTION THEN THE NEXT QUESTION YOU HAVE TO DO FASTER ...........................................................

Hmmmm .. interesting

So basically you`re deriving a function respect to other?

13:15 Not the case, because the derivative of 1/g(x) is not 1/g'(x).

I wonder why L'hopital's rule doesn't work in an arbitrary point where y! = 0. The graphs would be the same but shifted, so it seems to me that the rule should be also applicable. Why is that false?

@catharsis7629

2 жыл бұрын

Remember these graphs are not straight, the slope would be different in that reference frame.

@APaleDot

Жыл бұрын

Remember, we are taking the limit as x -> c, which means we can approximate the functions as if they are linear functions f(c) + f'(c)dx and g(c) + g'(c)dx as shown in the video. It works out so nicely in the video because f(c) = g(c) = 0, which means the ratio between these two approximations becomes (0 + f'(c)dx) / (0 + g'(c)dx) = f'(c)dx / g'(c)dx = f'(c) / g'(c). But consider the case where f(c) = g(c) ≠ 0. Then our limit turns out very differently because as x -> c, dx -> 0 and the ratio of the approximations becomes (f(c) + 0) / (g(c) + 0) = f(c) / g(c)

ONE OF MY FRIEND SAID TO ME ...... IF YOU FORGET FORMULA YOU HAVE TO LEARN HOW TO DERIVE THE FORMULA HOW TO PROVE THEOREM IN A QUICK WAY ...........

@derekowens

3 жыл бұрын

Yes! And this one makes so much sense if you understand that little diagram of the two functions and their slopes.

its might be easier just to use a Taylor series about x=c and L'Hospital falls off the page.

u should use desmos

THE PROBLEM ME AND MY FRIEND MAKE AN ARGUMENTS WHICH WAY LEARN QUICKER ...... EVERYTIME GO TO EXAMS ....... I LOST AT LEAST 5 MINUTES TO WRITE DOWN ALL THE MAIN IMPORTANT FORMULA BECAUSE SOMETIMES I FORGET FORGET FORMULA WHEN THE QUESTION IS TOO EASY TO SOLVE ..... REALLY ANNOY ...............

Flat earth society disagrees

Use Desmos!

Very instructive but please use the correct word. A demonstration or explanation but not a proof.

@derekowens

4 жыл бұрын

Okay, I see your point, and thanks. I do think, though, that the approach shown here is logically compelling, and in that sense it would qualify as a proof.

Um no ur actually wrong the earth is indeed flat.

@derekowens

5 жыл бұрын

Ah, that's good to know. Thanks for clearing that up for everyone. I'll tell my friend who is a pilot and I'm sure that will help him navigate over the north pole, if there even is such a thing. Oh, the silly delusions we would all believe if it weren't for the enlightenment provided here. I'm glad you've shared your wisdom for all of us to partake of.

@carsonholloway

5 жыл бұрын

@@derekowens I know, it sounds ridiculous at first, but believe me, I used to be as unaware as yourself. But one day, (a rainy Tuesday, to be specific), I had a realization that the government's notion of a spherical earth, and the moon landing, at that, are all dogmatic statements forced upon all the innocent, yet ignorant, members of society. Consider this for yourself; is it really worth the government to spend ~$21.5 billion /year on NASA, for them to make rockets and satellites, or for the supreme leaders of the world (including, but not limited to the members of the Illuminati) to have a spare ~$21 billion /year to continue and expand their operations (the other .5 billion /year is NASA's budget to fake the spherical earth "evidence"). Now, the first counterargument you may give is gravity forces the earth to collapse into itself and form a sphere. While it is true that gravity does exist, and it does keep the world from falling into pieces, (and this is the part where many of the "spherical" earth simpletons seem to get it wrong), a sphere is not the only way for a mass to be in equilibrium. If you have attended physics in modern day university, you will of course be taught that the earth is a sphere as the gravity pulls all the mass into some sort of stable structure, which is only sometimes a sphere; there are many other three dimensional shapes that can be in equilibrium, such as tori or discs. But, as you would have been aware if you weren't a believer of the false information fed to you by the authorities, the earth is obviously a disc. You may be familiar with Ockham's Razor, (originally "Entia non sunt multiplicanda praeter necessitatem", or commonly translated to "The simplest explanation is usually the best" or more literally "More things should not be used than are necessary"), and indeed, in this instance the simplest explanation is that the earth is a disc. The earth looks flat to you as you walk around, you don't notice the curvature, which leads to the much simpler explanation of the earth actually being flat. But instead the government said the earth was spherical, with little to no evidence, and everybody else believed them. I'm genuinely sorry for you, that you're living under a metaphorical rock, unbeknownst to the truth.

@carsonholloway

5 жыл бұрын

@@davidbandy6268 I'm not a flat-earther, I was just trying to give the most ridiculous sounding argument I could think of.

@davidbandy6268

5 жыл бұрын

@@carsonholloway I guess I was wrong, it's really sad how much of the world is existing totally oblivious to the lies of our government... And then people like you come along, get so close to the truth, and then just make fun of it because you are too weak to admit that you have been deceived. Unbelievable.

@carsonholloway

5 жыл бұрын

@@davidbandy6268 Give me your best argument for why the earth is flat and maybe you can change my mind.

the way you say "over" is so bizarre. Are you like an oldschool so-cal surfer?

@derekowens

Жыл бұрын

Haha! That's pretty funny. I grew up on the east coast, and while I didn't do much surfing I did watch Fast Times at Ridgemont High...

2:40 The world is flat!! Get it right n do ur own research we aint no globe! 🙄

@derekowens

3 жыл бұрын

The earth is flat ...if you zoom in enough!

I'm an UG B.tech 1st year student. I've already realized this proof during studying the Thomas's calculus book. And many other proofs like this also I have realized by myself. I think I am a different student. What is the best thing I should do? Because I am confused about my career. Can you tell me what is best for me ? (Currently I am an electrical engineering UG student)

@REL1C

5 жыл бұрын

Getting off KZread and finding a passion would be a good start.

Thank you