The most soluble and miscible proof and the smoothest of logical derivation for a simplified,yet atomic scale interpretation and visualization. Absolutely stupendous!!!
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! :)
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.
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
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.
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?
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.
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
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.
Well, this really helps understand the basics of lhospitals, but i got a doubt. In the proof, in the division by (x-a) should be possible. Since, if x tends to 0 , (x-a)=0. Idk, is it possible since its tending to a and not a. Please help solve this doubt.
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
The most soluble and miscible proof and the smoothest of logical derivation for a simplified,yet atomic scale interpretation and visualization. Absolutely stupendous!!!
The handwriting is perfect makes everything so clear
Thanks
You're very funny
It helps relieve the tension and increase understanding
I can rewatch and laugh while learning 😅
Short, sweet and effective. Many thanks.
😊
Hands down best proof on the internet. Thank you so much!
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! :)
One of the best proof i have seen so far, Not even involved Mean value theorem here.
You are an excellent teacher. God bless you.
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.
Thanks sir , Ur teaching method is awesome
This is the first time I am seeing the proof of L'Hospital rule.
Thanks very much.
Your teaching method is very good
Destiny helper indeed. thanks dear sir.
really useful and not complicated , Thanks sir
Thanks man i hope you get the views u deserve helped alot ❤️
Amazing explantion! It helped me a lot to undertand the concept and solve my limits homework! Thank you so much and keep doing it!
Oh my God, thank you so much! This video helped me understand the proof so much more easily! Thank you! Fantastic video!
Beautifully explained. Thank you so much
This proof is so clear and simple that a caveman can understand it. Kudos, and thanks for sharing.
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
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.
A very nice explanation!
Very clear and emotional explanation😂, thank u so much!
Such an elegant proof! 😮
Thank you so much for this video it has helped me so much, glad you made it :)
I always thought this was hard to prove, great explanation. Thanks for the video 👍
Wow , a perfect lecture. Thank you.
Fantastic video ❤️❤️
Wow. This was super easy to understand. Well done, sir!
Clear explanations, easy to grasp ;)
You absolutely blow my mind i was just do Differentiation and it makes for sence to see the formula to pop up like that.
YOU ARE REALLY GOOD SIR, THANKS
Great work friend 😮
Nice to know that this is clearly from differentiation from first principle.
The best explanation I've seen so far
Thank you! Awesome proof.
Yes. Thank you so much ❤️
Excellent explanation Sir. Thanks 👍
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
Thank you so much! Your video is so helpful!
Beautiful proof
Wow, this is super clear.
Very simple and brilliant proof.
What an elegant proof!
A simple proof. Thank you
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
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
Math is beautiful! Thank you 🦋
Very good explanation bro....your looking very cool best of luck
"You cannot write zero over zero, any time, anywhere."
YOU JUST DID
Oh nooooo!🤣🤣🤣🤣🤣
thank you sooo much sir this video is helpful for me
Flawless, I love it.
Just LOVE IT! Thanks.
Powerful 🙏🏿👍🏾❤
Excellent Video!
Thank you very much!
Can't believe i lost 8 marks for such a simple proof😭😭
Tshwarelo. Phephisa ngwana ntate.
Tu es top mon cher Newton !
It's SUPERB and really simplified..... thnnx
This was very helpful, thanks!
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.
So precise
Thnk you.....have understood now
BEAUTIFUL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
excellent👏👏👏👏
The proof is as smart as your cap.
That Bernoulli was one clever chap!😃
thank you sir _/\_ amazing explanation, i wassearching for this
good explainations
I love you THIS HELPED ME SO MUCH 😊😊😊😊
😘😘😘❤️💕💕💯😋🤣💜💙❤️😍❤️🔥
Wow very useful!!! Thank you
Well done
Nice proof. 9:59 Aye. I've seen this before!
Beautiful
What about ±∞/∞ indeterminant form?? We need a proof for that too because L’Hôpital’s Rule also works for this indeterminant…
amazing proof
Beautiful 🎉
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.
🎉 Great 👍. Thank You. Regards.
Thank you!
You're welcome!
Thank you mister
Very helpful
Clean Hands ...perfect proof .
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.
WOW 😳👏 definitely subscribing thanks a whole lot🙌
Legend
It was just amazing
Thank you, sir 😊
You're welcome!
I have one concern, how do you know that f and g are differentiable at x=a?
Thanks so much sir. (What infinity ÷infinity case) 0/0 is just one of them
thank you very much!!
Dividing by x-a, here, seems disturbingly close to zero division - but I suppose that's what differentiation always is, anyway. ;)
Thanks!
Thank you!
That was great!
Well, this really helps understand the basics of lhospitals, but i got a doubt. In the proof, in the division by (x-a) should be possible. Since, if x tends to 0 , (x-a)=0. Idk, is it possible since its tending to a and not a. Please help solve this doubt.
I like your lesson,can you show us how to draw the graph of equation of asymptote
Asymptote to what function?
Email me a problem
Good, indeed.
🔥🔥
goat