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 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 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
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.
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 !
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 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).
@@PrimeNewtons I do like the proof. Can you do another video with the rigorous proof? Also one that handles infinity / infinity and the other variations? You do such a magnificent job of presenting, sir! 😃
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.
Better proof and correct oroff involves MEAN VALUE THEOREM : f(x) = f'(x)(x-a), and g(x) =g'(x)(x-a) then a bit of simple algebra yields limit as x approaches a of f'(x)/g'(x) and not simply f'(x)/g'(x).
A really amazing proof But what about the infinity by infinity form😕😕 Also I had a question Say the indertiminate form 1^♾️ For ex a lim g(x) ^f(x) Now say f(a) = 0/0 However it's f'(a) is infinity And g(a) is infinity Then should we apply the standard limit of 1^♾️ form
The only kind of small concern is that for the new limit to be equal to(f(a))'/(g(a))' it probably has yo assume that it is not an indefinite form,but again im not so sure if this is a problem
Wait! I though that L'Hopital rule given that f(a)=g(a) =0 or = +/- infinite states: Limit as x approaches a of f(x)/g(x) is the same as lim as x approaches a of f'(x)/g'(x), not what you result say, that is, f'(a)/g'(a).....?
Hands down best proof on the internet. Thank you so much!
Thank you! I’ve had difficulty in understanding L’hopital’s rule, and your tutorial is a big step in the right direction.
The most soluble and miscible proof and the smoothest of logical derivation for a simplified,yet atomic scale interpretation and visualization. Absolutely stupendous!!!
Superb Mr Newton. Never seen such simple proof like this.
You are making calculus look like driving a car❤.
God bless
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.
😊
Destiny helper indeed. thanks dear sir.
Thanks sir , Ur teaching method is awesome
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 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.
One of the best proof i have seen so far, Not even involved Mean value theorem here.
Your teaching method is very good
Oh my God, thank you so much! This video helped me understand the proof so much more easily! Thank you! Fantastic video!
Thank you so much for this video it has helped me so much, glad you made it :)
You are an excellent teacher. God bless you.
Amazing explantion! It helped me a lot to undertand the concept and solve my limits homework! Thank you so much and keep doing it!
This is the first time I am seeing the proof of L'Hospital rule.
Thanks very much.
really useful and not complicated , Thanks sir
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 man i hope you get the views u deserve helped alot ❤️
Nice to know that this is clearly from differentiation from first principle.
I always thought this was hard to prove, great explanation. Thanks for the video 👍
You absolutely blow my mind i was just do Differentiation and it makes for sence to see the formula to pop up like that.
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?
Correct!
@@christophvonpezold4699 Yes
Yes. Thank you so much ❤️
Beautifully explained. Thank you so much
A very nice explanation!
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
Such an elegant proof! 😮
Very clear and emotional explanation😂, thank u so much!
Wow , a perfect lecture. Thank you.
Excellent explanation Sir. Thanks 👍
YOU ARE REALLY GOOD SIR, THANKS
Clear explanations, easy to grasp ;)
Fantastic video ❤️❤️
Thank you so much! Your video is so helpful!
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
Very simple and brilliant proof.
Thank you! Awesome proof.
Beautiful proof
Wow. This was super easy to understand. Well done, sir!
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.
Can't believe i lost 8 marks for such a simple proof😭😭
Tshwarelo. Phephisa ngwana ntate.
What an elegant proof!
Great work friend 😮
Just LOVE IT! Thanks.
A simple proof. Thank you
This was very helpful, thanks!
Wow, this is super clear.
Excellent Video!
Thank you very much!
The best explanation I've seen so far
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.
Powerful 🙏🏿👍🏾❤
Thnk you.....have understood now
Math is beautiful! Thank you 🦋
Very good explanation bro....your looking very cool best of luck
thank you sooo much sir this video is helpful for me
excellent👏👏👏👏
Tu es top mon cher Newton !
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).
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.
thank you sir _/\_ amazing explanation, i wassearching for this
Nice proof! So, why did you put proof in quotes in the title of the video?
Some would say it's not rigorous
@@PrimeNewtons I do like the proof. Can you do another video with the rigorous proof? Also one that handles infinity / infinity and the other variations? You do such a magnificent job of presenting, sir! 😃
I love you THIS HELPED ME SO MUCH 😊😊😊😊
😘😘😘❤️💕💕💯😋🤣💜💙❤️😍❤️🔥
Beautiful
Thank you!
You're welcome!
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.
BEAUTIFUL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
What about ±∞/∞ indeterminant form?? We need a proof for that too because L’Hôpital’s Rule also works for this indeterminant…
It's SUPERB and really simplified..... thnnx
Beautiful 🎉
WOW 😳👏 definitely subscribing thanks a whole lot🙌
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
Well done
I have one concern, how do you know that f and g are differentiable at x=a?
Nice proof. 9:59 Aye. I've seen this before!
Better proof and correct oroff involves MEAN VALUE THEOREM : f(x) = f'(x)(x-a), and g(x) =g'(x)(x-a) then a bit of simple algebra yields limit as x approaches a of f'(x)/g'(x) and not simply f'(x)/g'(x).
"You cannot write zero over zero, any time, anywhere."
YOU JUST DID
Oh nooooo!🤣🤣🤣🤣🤣
Very helpful
amazing proof
🎉 Great 👍. Thank You. Regards.
thank you very much!!
Thank you mister
The proof is as smart as your cap.
That Bernoulli was one clever chap!😃
Thanks!
Thank you!
A really amazing proof
But what about the infinity by infinity form😕😕
Also I had a question
Say the indertiminate form
1^♾️
For ex a lim g(x) ^f(x)
Now say f(a) = 0/0
However it's f'(a) is infinity
And g(a) is infinity
Then should we apply the standard limit of 1^♾️ form
Your question is interesting. Please email picture of the written question to me. primenewtons@gmail.com. Or just message me on Instagram.
@@PrimeNewtons I don't have Instagram so I mailed it to you
The only kind of small concern is that for the new limit to be equal to(f(a))'/(g(a))' it probably has yo assume that it is not an indefinite form,but again im not so sure if this is a problem
If it produces another indeterminate form, then L'Hospitals rule should be applied over and over until no such indeterminate form is produced.
Wait! I though that L'Hopital rule given that f(a)=g(a) =0 or = +/- infinite states: Limit as x approaches a of f(x)/g(x) is the same as
lim as x approaches a of f'(x)/g'(x), not what you result say, that is, f'(a)/g'(a).....?
Clean Hands ...perfect proof .
good explainations
Great proof! But I wonder what if f(a)=g(a)=∞? ∞/∞ is also a indeterminate.
You do it again
You should uae "=" equal not the "=>" if then.. infact every line should started with " " if and only if
how do u prove the generalized version
That would be in analysis. Not yet in my scope of videos.
Good, indeed.
Legend
That was great!
Thank you, sir 😊
You're welcome!
thanks !