The most soluble and miscible proof and the smoothest of logical derivation for a simplified,yet atomic scale interpretation and visualization. Absolutely stupendous!!!
I'm a math teacher myself and I have made it a point in my career to also have exemplary handwriting. It makes math easier to follow for students if they are not guessing what you just wrote on the board. His explanations are clear, his pacing is perfect, he gives context before diving in. This guy is a natural. I only assume he's a college professor/high school teacher.
I love the proof. It is an ‘ if A, then B’ proof. You start with part of B and jump back to A and use that information to rewrite the expression. When the rewriting from A maths the writing of B, the proof is done. Thank you Doctor. The proof is simple and shiny. Looking forward to the next proof.
Just as I was trying to understand better L'hopital rule I found your proof, really helped me understand by using the definition of derivative with lim, tysm, wish you the best! :)
thank you for making this the exact information i was looking for, ive watched like 10 different videos on this and they are all too complicated, too fast, or too long to get to the point, your video answered a lot of questions i had that nobody elses videos were covering
Thank you so much! this really helped me understand the rule and it's a really elegant proof, and in general your channel is incredible and I cannot believe you don't have more subscribers. However, I've heard that l'hopital's rule works in other cases besides 0/0 like for example infinity*infinity - have I been misinformed or is there some way to further derive other applications of the rule?
Thank you. I hope some day the channels grows sufficiently. Yes it works for any of 'the seven deadly sins'. I have a video of all 7 forms. However, the function must be rewritten as a rational function to apply L"Hospital.
@@PrimeNewtons ah ok, good to know - I actually did watch your seven sins video, so what your saying is that basically all indeterminate forms in some way are derived from 0/0 and as such can have l’hopital’s rule applied to them if expressed as a quotient?
Share a thought? This theorem requires a vivid demonstration for a memory-able understanding. May i suggest the following. Sketch -graph on board: Draw f(x) which is dome -shaped and going through zero at x=a. Also on the same graph, sketch the corresponding f' (x) ; of course with f ' (a)= zero. ..... then also draw th same for a carefully selected g(x).. discuss. what you see. ... Good luck, and have god time having such an enviable job.....suresh
Dear sir. Very Good evening. The explanation part is excellent. The spelling of the rule is to be corrected as I guess. It is L'HOPITAL'S RULE with a hat symbol over O.
You should have seen how my jaw nearly fell off my face at the end when everything for the proof of L'hopital's rule comes together. I just got no words since my jaw is on the floor except that there should be a trigger warning for this. A Trigger Warning to warn people that there jaw will be on the floor for the simplicity and comprehensive nature of the proof
This is the proof for the application of L'Hopital's to limits of the form 0/0. Would be nice to see the proof for when the limit is of the form ±∞/±∞?
I just was umaware of the division law of limits and the notation of derivative: f(x) - f(a)/ x-a to be eqaul to the derivative of the function evaluated at a. Would you please recommend me any video of yours so that I may better grasp on this?
Thank you for this explanation! Can you give us any function which needs another application of l'Hospital's rule ? And by the way your handwriting is nice !
Great video! But I miss some explanation about the limit ∞/∞. (and the rule of Hospital is that you go there, when you're ill. You use Hopital for math).
Alright, theres just one important caveat. What if lim x->a f/g is not indeterminate like 0/0? What if it’s defined like 5 or 6. You might think you can use l’hopital anyway. Well it turns out you cannot. The reason is very subtle. If the limit is not indeterminate, then the limit of f/g is the same as when you evaluate f/g at exactly a. We can write the ratio of the derivatives as lim x->a (f(x)-f(a)/g(x)-g(a) )(x-a)/(x-a). The reason that I’m doing this, is that when I evaluate x at a, we get 0/0. This means that we get an undefined result for when we evaluate defined limits. This is quite important to mention.
this only holds for when the functions are continuous right? because first and the most obvious u cannot differentiate it if its not continuous and also if it is discontinuous f(a) or g(a) need not be equal to 0 just their limiting values can be 0?
I believe in L'Hopital's rule, and I believe in your proof. I am still working on understanding why it makes sense in concept, and I'm almost there. If both numerator and denominator are racing toward infinity, the question is which one gets there faster. In other words, how do their derivatives compare. And since we're heading to infinity, any finite conditions (for example, a constant added to the top or bottom) cease to matter. I think my logic holds up. But when it's 0/0, my logic is a little flimsier. I feel like, if your function is approaching zero, then the reciprocal of your function is approaching infinity, so the same "infinity" logic might apply. But I haven't convinced myself that it's a valid argument.
Brief and simple. Hands down one of the most excellent proof, sir
Thank you! I’ve had difficulty in understanding L’hopital’s rule, and your tutorial is a big step in the right direction.
Superb Mr Newton. Never seen such simple proof like this.
You are making calculus look like driving a car❤.
God bless
This dude is the best math teacher on the Internet. Born to do this.
The most soluble and miscible proof and the smoothest of logical derivation for a simplified,yet atomic scale interpretation and visualization. Absolutely stupendous!!!
Can't believe i lost 8 marks for such a simple proof😭😭
Tshwarelo. Phephisa ngwana ntate.
The handwriting is perfect makes everything so clear
Thanks
I'm a math teacher myself and I have made it a point in my career to also have exemplary handwriting. It makes math easier to follow for students if they are not guessing what you just wrote on the board. His explanations are clear, his pacing is perfect, he gives context before diving in. This guy is a natural. I only assume he's a college professor/high school teacher.
One of the best proof i have seen so far, Not even involved Mean value theorem here.
I love the proof. It is an ‘ if A, then B’ proof. You start with part of B and jump back to A and use that information to rewrite the expression. When the rewriting from A maths the writing of B, the proof is done.
Thank you Doctor. The proof is simple and shiny.
Looking forward to the next proof.
Just as I was trying to understand better L'hopital rule I found your proof, really helped me understand by using the definition of derivative with lim, tysm, wish you the best! :)
This is the first time I am seeing the proof of L'Hospital rule.
Thanks very much.
You're very funny
It helps relieve the tension and increase understanding
I can rewatch and laugh while learning 😅
I watch videos on maths on different channels. But found your explanation very impressive and simple.
You are an excellent teacher. God bless you.
Short, sweet and effective. Many thanks.
😊
Your teaching method is very good
Thanks sir , Ur teaching method is awesome
Amazing explantion! It helped me a lot to undertand the concept and solve my limits homework! Thank you so much and keep doing it!
thank you for making this the exact information i was looking for, ive watched like 10 different videos on this and they are all too complicated, too fast, or too long to get to the point, your video answered a lot of questions i had that nobody elses videos were covering
Oh my God, thank you so much! This video helped me understand the proof so much more easily! Thank you! Fantastic video!
really useful and not complicated , Thanks sir
Thanks man i hope you get the views u deserve helped alot ❤️
Thanks a lot for this clear explanation and helping me in the middle of the night 😊
Thank you,teacher.Hello from Turkey!
Beautifully explained. Thank you so much
Destiny helper indeed. thanks dear sir.
Very clear and emotional explanation😂, thank u so much!
Wow. This was super easy to understand. Well done, sir!
I always thought this was hard to prove, great explanation. Thanks for the video 👍
U’re def going to save my grades this semester❤
You're the best thank you 🎉🎉🎉
Thank you so much for this video it has helped me so much, glad you made it :)
You absolutely blow my mind i was just do Differentiation and it makes for sence to see the formula to pop up like that.
What about ±∞/∞ indeterminant form?? We need a proof for that too because L’Hôpital’s Rule also works for this indeterminant…
Such an elegant proof! 😮
A very nice explanation!
Nice to know that this is clearly from differentiation from first principle.
Thanks for ur video, you makes math becomes so simple!!!!
Fantastic video ❤️❤️
Damn, the derivation of l'hospitals rule was very elegant
Very good explanation bro....your looking very cool best of luck
Thank you so much! this really helped me understand the rule and it's a really elegant proof, and in general your channel is incredible and I cannot believe you don't have more subscribers. However, I've heard that l'hopital's rule works in other cases besides 0/0 like for example infinity*infinity - have I been misinformed or is there some way to further derive other applications of the rule?
Thank you. I hope some day the channels grows sufficiently. Yes it works for any of 'the seven deadly sins'. I have a video of all 7 forms. However, the function must be rewritten as a rational function to apply L"Hospital.
@@PrimeNewtons ah ok, good to know - I actually did watch your seven sins video, so what your saying is that basically all indeterminate forms in some way are derived from 0/0 and as such can have l’hopital’s rule applied to them if expressed as a quotient?
Correct!
@@christophvonpezold4699 Yes
Great work friend 😮
Wow , a perfect lecture. Thank you.
Excellent explanation Sir. Thanks 👍
Thanks for saving my mental health
The best explanation I've seen so far
Thank you so much! Your video is so helpful!
Share a thought? This theorem requires a vivid demonstration for a memory-able understanding. May i suggest the following. Sketch -graph on board: Draw f(x) which is dome -shaped and going through zero at x=a. Also on the same graph, sketch the corresponding f' (x) ; of course with f ' (a)= zero. ..... then also draw th same for a carefully selected g(x).. discuss. what you see. ... Good luck, and have god time having such an enviable job.....suresh
Clear explanations, easy to grasp ;)
YOU ARE REALLY GOOD SIR, THANKS
Thanks!
Thank you!
Nicely, nicely! Well done!
Very simple and brilliant proof.
Yes. Thank you so much ❤️
"You cannot write zero over zero, any time, anywhere."
YOU JUST DID
Oh nooooo!🤣🤣🤣🤣🤣
Dear sir.
Very Good evening.
The explanation part is excellent.
The spelling of the rule is to be corrected as I guess.
It is L'HOPITAL'S RULE with a hat symbol over O.
I've seen that spelling too. I suppose we do what we like these days.
hello! he used to write his own name with an s. that ô replaced the silent s
Thank you! Awesome proof.
Thanks for the help ❤from Nepal
What an elegant proof!
you are the best sir
Math is beautiful! Thank you 🦋
A simple proof. Thank you
I love you THIS HELPED ME SO MUCH 😊😊😊😊
😘😘😘❤️💕💕💯😋🤣💜💙❤️😍❤️🔥
Wow, this is super clear.
Beautiful proof
You should have seen how my jaw nearly fell off my face at the end when everything for the proof of L'hopital's rule comes together. I just got no words since my jaw is on the floor except that there should be a trigger warning for this.
A Trigger Warning to warn people that there jaw will be on the floor for the simplicity and comprehensive nature of the proof
It's SUPERB and really simplified..... thnnx
Powerful 🙏🏿👍🏾❤
The proof is as smart as your cap.
That Bernoulli was one clever chap!😃
excellent👏👏👏👏
Actually, as long as both the numerator and denominator both reaches 0 or +- infinity it would be good. Proof is a bit longer but similar in the end.
Tu es top mon cher Newton !
thank you sooo much sir this video is helpful for me
Do this proof in a math class 1 exam, you will get zero obviously. But if you do this proof in a k12 class, they will think that you are genius
you nailed it bro, thank you so much
This is the proof for the application of L'Hopital's to limits of the form 0/0.
Would be nice to see the proof for when the limit is of the form ±∞/±∞?
Excellent Video!
Thank you very much!
thank you sir _/\_ amazing explanation, i wassearching for this
Flawless, I love it.
WOW 😳👏 definitely subscribing thanks a whole lot🙌
Thank you, I can understand it now, thank you so much
I just was umaware of the division law of limits and the notation of derivative: f(x) - f(a)/ x-a to be eqaul to the derivative of the function evaluated at a. Would you please recommend me any video of yours so that I may better grasp on this?
Nice proof. 9:59 Aye. I've seen this before!
Just LOVE IT! Thanks.
This was very helpful, thanks!
Thnk you.....have understood now
Thank you for this explanation! Can you give us any function which needs another application of l'Hospital's rule ? And by the way your handwriting is nice !
Thank you for your kind words. Another video coming later today.
I have one concern, how do you know that f and g are differentiable at x=a?
Great video! But I miss some explanation about the limit ∞/∞.
(and the rule of Hospital is that you go there, when you're ill. You use Hopital for math).
Alright, theres just one important caveat. What if lim x->a f/g is not indeterminate like 0/0? What if it’s defined like 5 or 6. You might think you can use l’hopital anyway. Well it turns out you cannot. The reason is very subtle.
If the limit is not indeterminate, then the limit of f/g is the same as when you evaluate f/g at exactly a. We can write the ratio of the derivatives as lim x->a (f(x)-f(a)/g(x)-g(a) )(x-a)/(x-a). The reason that I’m doing this, is that when I evaluate x at a, we get 0/0. This means that we get an undefined result for when we evaluate defined limits. This is quite important to mention.
this only holds for when the functions are continuous right? because first and the most obvious u cannot differentiate it if its not continuous and also if it is discontinuous f(a) or g(a) need not be equal to 0 just their limiting values can be 0?
BEAUTIFUL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
I believe in L'Hopital's rule, and I believe in your proof. I am still working on understanding why it makes sense in concept, and I'm almost there.
If both numerator and denominator are racing toward infinity, the question is which one gets there faster. In other words, how do their derivatives compare. And since we're heading to infinity, any finite conditions (for example, a constant added to the top or bottom) cease to matter. I think my logic holds up.
But when it's 0/0, my logic is a little flimsier. I feel like, if your function is approaching zero, then the reciprocal of your function is approaching infinity, so the same "infinity" logic might apply. But I haven't convinced myself that it's a valid argument.
I would suggest looking at 3blue1brown's video about L'Hospital's rule. He uses a lot of visuals to help you intuitively understand calculus concepts.
thank you very much!!
Wow very useful!!! Thank you
🎉 Great 👍. Thank You. Regards.
Excellent teacher
please make a video to explain Rolle's theorem
👍
I apologize for the delay. I should make a video or Rolle's theorem soon.
good explainations
Beautiful 🎉