'Proof' of L'Hospital's Rule

  Рет қаралды 21,067

Prime Newtons

Prime Newtons

2 жыл бұрын

In this video I showed a simplified 'proof' of L'Hoc pital's Rule using the definition of the derivative.

Пікірлер: 159
@prostatecancergaming9531
@prostatecancergaming9531 2 жыл бұрын
Hands down best proof on the internet. Thank you so much!
@BeauGeorge
@BeauGeorge 9 ай бұрын
Thank you! I’ve had difficulty in understanding L’hopital’s rule, and your tutorial is a big step in the right direction.
@hasinmazumder8123
@hasinmazumder8123 3 ай бұрын
The most soluble and miscible proof and the smoothest of logical derivation for a simplified,yet atomic scale interpretation and visualization. Absolutely stupendous!!!
@utuberaj60
@utuberaj60 Жыл бұрын
Superb Mr Newton. Never seen such simple proof like this. You are making calculus look like driving a car❤. God bless
@jysusplash
@jysusplash 9 ай бұрын
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! :)
@aniarinze8269
@aniarinze8269 8 ай бұрын
You're very funny It helps relieve the tension and increase understanding I can rewatch and laugh while learning 😅
@BrandenTea
@BrandenTea 4 ай бұрын
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
@johnroberts7529
@johnroberts7529 8 ай бұрын
Short, sweet and effective. Many thanks. 😊
@HenriqueOliveira-so6um
@HenriqueOliveira-so6um 2 жыл бұрын
Amazing explantion! It helped me a lot to undertand the concept and solve my limits homework! Thank you so much and keep doing it!
@aseruajanifer7687
@aseruajanifer7687 2 ай бұрын
Destiny helper indeed. thanks dear sir.
@haseebomer8729
@haseebomer8729 2 жыл бұрын
Thanks man i hope you get the views u deserve helped alot ❤️
@perspicacity89
@perspicacity89 2 жыл бұрын
Oh my God, thank you so much! This video helped me understand the proof so much more easily! Thank you! Fantastic video!
@atulsingh890
@atulsingh890 7 ай бұрын
One of the best proof i have seen so far, Not even involved Mean value theorem here.
@cherryisripe3165
@cherryisripe3165 7 ай бұрын
You are an excellent teacher. God bless you.
@jensberling2341
@jensberling2341 5 ай бұрын
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.
@user-iz9ql7py9j
@user-iz9ql7py9j 8 ай бұрын
Thanks sir , Ur teaching method is awesome
@naimamiola6231
@naimamiola6231 2 жыл бұрын
Thank you so much for this video it has helped me so much, glad you made it :)
@theadvancemathshub
@theadvancemathshub 2 жыл бұрын
Your teaching method is very good
@EE-Spectrum
@EE-Spectrum 2 жыл бұрын
This is the first time I am seeing the proof of L'Hospital rule. Thanks very much.
@Bedoroski
@Bedoroski Жыл бұрын
Beautifully explained. Thank you so much
@trubblman
@trubblman 4 ай бұрын
Wow. This was super easy to understand. Well done, sir!
@kub8675
@kub8675 2 ай бұрын
I always thought this was hard to prove, great explanation. Thanks for the video 👍
@magdishan8729
@magdishan8729 2 жыл бұрын
really useful and not complicated , Thanks sir
@kawambwadaniel-kd3685
@kawambwadaniel-kd3685 Жыл бұрын
The handwriting is perfect makes everything so clear
@PrimeNewtons
@PrimeNewtons Жыл бұрын
Thanks
@nitorikinni488
@nitorikinni488 2 жыл бұрын
Nice to know that this is clearly from differentiation from first principle.
@cke166
@cke166 Жыл бұрын
Very clear and emotional explanation😂, thank u so much!
@derekbaugh6360
@derekbaugh6360 2 жыл бұрын
Wow , a perfect lecture. Thank you.
@kyon5951
@kyon5951 Жыл бұрын
Thank you so much! Your video is so helpful!
@awusacollins
@awusacollins 7 ай бұрын
Clear explanations, easy to grasp ;)
@lucdhomme3105
@lucdhomme3105 2 жыл бұрын
A very nice explanation!
@kingonion2102
@kingonion2102 8 ай бұрын
Such an elegant proof! 😮
@surendrakverma555
@surendrakverma555 4 ай бұрын
Excellent explanation Sir. Thanks 👍
@genogurirab8061
@genogurirab8061 2 жыл бұрын
You absolutely blow my mind i was just do Differentiation and it makes for sence to see the formula to pop up like that.
@kingbeauregard
@kingbeauregard Жыл бұрын
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.
@ZipplyZane
@ZipplyZane Жыл бұрын
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.
@reyadhaloraibi3387
@reyadhaloraibi3387 6 ай бұрын
Very simple and brilliant proof.
@ripadebsharma3268
@ripadebsharma3268 2 жыл бұрын
It's SUPERB and really simplified..... thnnx
@SanjeevKumar-ld4iv
@SanjeevKumar-ld4iv 6 ай бұрын
Very good explanation bro....your looking very cool best of luck
@spacetimemalleable7718
@spacetimemalleable7718 24 күн бұрын
Just LOVE IT! Thanks.
@777mehran
@777mehran Жыл бұрын
Thank you! Awesome proof.
@SAbibuKettor
@SAbibuKettor 7 ай бұрын
YOU ARE REALLY GOOD SIR, THANKS
@locvaomat1313
@locvaomat1313 2 жыл бұрын
Yes. Thank you so much ❤️
@krss5282
@krss5282 2 жыл бұрын
Fantastic video ❤️❤️
@usmansubhani
@usmansubhani 6 ай бұрын
What an elegant proof!
@shuaibjemil
@shuaibjemil 2 жыл бұрын
Wow, this is super clear.
@GobackTostudy
@GobackTostudy 2 ай бұрын
thank you sir _/\_ amazing explanation, i wassearching for this
@christophvonpezold4699
@christophvonpezold4699 Жыл бұрын
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?
@PrimeNewtons
@PrimeNewtons Жыл бұрын
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.
@christophvonpezold4699
@christophvonpezold4699 Жыл бұрын
@@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?
@PrimeNewtons
@PrimeNewtons Жыл бұрын
Correct!
@PrimeNewtons
@PrimeNewtons Жыл бұрын
@@christophvonpezold4699 Yes
@hypersonic6649
@hypersonic6649 5 ай бұрын
Beautiful proof
@fabianstefanus-ye3yz
@fabianstefanus-ye3yz Жыл бұрын
The best explanation I've seen so far
@levysarah2954
@levysarah2954 5 ай бұрын
Tu es top mon cher Newton !
@misozitortoise-vv4xe
@misozitortoise-vv4xe 5 ай бұрын
WOW 😳👏 definitely subscribing thanks a whole lot🙌
@sandip7448
@sandip7448 Жыл бұрын
thank you sooo much sir this video is helpful for me
@prof.cesararmas6325
@prof.cesararmas6325 3 ай бұрын
Beautiful 🎉
@AliciaMarkoe
@AliciaMarkoe 5 ай бұрын
Math is beautiful! Thank you 🦋
@thomasblackwell9507
@thomasblackwell9507 8 ай бұрын
BEAUTIFUL!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
@rprsto
@rprsto 6 ай бұрын
Beautiful
@mathswithNulaksha
@mathswithNulaksha 9 ай бұрын
thank you very much!!
@omphilenxeku8999
@omphilenxeku8999 2 жыл бұрын
Powerful 🙏🏿👍🏾❤
@manjumukundanjayakumar8460
@manjumukundanjayakumar8460 Жыл бұрын
A simple proof. Thank you
@briahcherotich2782
@briahcherotich2782 Жыл бұрын
Thnk you.....have understood now
@Matematicand01
@Matematicand01 6 ай бұрын
That was great!
@AliAhmad-si4fb
@AliAhmad-si4fb 2 ай бұрын
🎉 Great 👍. Thank You. Regards.
@patricialowenstaff5136
@patricialowenstaff5136 9 ай бұрын
Excellent Video!
@PrimeNewtons
@PrimeNewtons 9 ай бұрын
Thank you very much!
@sureshdave7
@sureshdave7 2 ай бұрын
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
@AubreyForever
@AubreyForever 8 ай бұрын
Very helpful
@segayanmx4442
@segayanmx4442 Жыл бұрын
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 !
@PrimeNewtons
@PrimeNewtons Жыл бұрын
Thank you for your kind words. Another video coming later today.
@ahmedabtahi1217
@ahmedabtahi1217 6 ай бұрын
good vid man keep it up
@fluffysony
@fluffysony Ай бұрын
amazing proof
@monaztaoui8067
@monaztaoui8067 4 ай бұрын
Thank you mister
@yuriyuri05
@yuriyuri05 Жыл бұрын
I love you THIS HELPED ME SO MUCH 😊😊😊😊
@PrimeNewtons
@PrimeNewtons Жыл бұрын
😘😘😘❤️💕💕💯😋🤣💜💙❤️😍❤️‍🔥
@mohammad.r.kamalabadi
@mohammad.r.kamalabadi Жыл бұрын
excellent👏👏👏👏
@ericcarvalhoferreira512
@ericcarvalhoferreira512 2 ай бұрын
Thank you!
@PrimeNewtons
@PrimeNewtons 2 ай бұрын
You're welcome!
@mathtips877
@mathtips877 Жыл бұрын
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.
@PrimeNewtons
@PrimeNewtons Жыл бұрын
I've seen that spelling too. I suppose we do what we like these days.
@waltz251
@waltz251 7 ай бұрын
hello! he used to write his own name with an s. that ô replaced the silent s
@Northeast1
@Northeast1 Жыл бұрын
good explainations
@thomasgreene5750
@thomasgreene5750 Жыл бұрын
Well done
@kingbeauregard
@kingbeauregard Жыл бұрын
"You cannot write zero over zero, any time, anywhere." YOU JUST DID
@PrimeNewtons
@PrimeNewtons Жыл бұрын
Oh nooooo!🤣🤣🤣🤣🤣
@stefanstathakis1681
@stefanstathakis1681 2 жыл бұрын
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
@PrimeNewtons
@PrimeNewtons 2 жыл бұрын
If it produces another indeterminate form, then L'Hospitals rule should be applied over and over until no such indeterminate form is produced.
@c.m.p2943
@c.m.p2943 Жыл бұрын
Thank you, sir 😊
@PrimeNewtons
@PrimeNewtons Жыл бұрын
You're welcome!
@chienbin4813
@chienbin4813 3 ай бұрын
thanks !
@HamisMohamed-hh2br
@HamisMohamed-hh2br Жыл бұрын
I like your lesson,can you show us how to draw the graph of equation of asymptote
@PrimeNewtons
@PrimeNewtons Жыл бұрын
Asymptote to what function? Email me a problem
@BeauGeorge
@BeauGeorge 9 ай бұрын
Thanks!
@PrimeNewtons
@PrimeNewtons 8 ай бұрын
Thank you!
@keithrobinson2941
@keithrobinson2941 Жыл бұрын
Nice proof. 9:59 Aye. I've seen this before!
@michaelhanford8139
@michaelhanford8139 Жыл бұрын
The proof is as smart as your cap. That Bernoulli was one clever chap!😃
@KBhunterx262
@KBhunterx262 Жыл бұрын
Legend
@hansvangiessen8395
@hansvangiessen8395 6 ай бұрын
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).
@pchan6305
@pchan6305 Жыл бұрын
Excellent teacher please make a video to explain Rolle's theorem
@PrimeNewtons
@PrimeNewtons Жыл бұрын
👍
@PrimeNewtons
@PrimeNewtons Жыл бұрын
I apologize for the delay. I should make a video or Rolle's theorem soon.
@elainekr9282
@elainekr9282 6 ай бұрын
Clean Hands ...perfect proof .
@joyneelrocks
@joyneelrocks 7 ай бұрын
What about ±∞/∞ indeterminant form?? We need a proof for that too because L’Hôpital’s Rule also works for this indeterminant…
@dhruvpoojary4567
@dhruvpoojary4567 24 күн бұрын
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.
@nebalsadek8881
@nebalsadek8881 6 ай бұрын
🔥🔥
@voixdeville7095
@voixdeville7095 6 ай бұрын
i love that
@JohnSmith-mz7dh
@JohnSmith-mz7dh 7 ай бұрын
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.
@wilsonoliveira7447
@wilsonoliveira7447 7 ай бұрын
Good, indeed.
@nothingbutmathproofs7150
@nothingbutmathproofs7150 7 ай бұрын
I have one concern, how do you know that f and g are differentiable at x=a?
@erikstrand2976
@erikstrand2976 Жыл бұрын
Now, this is the good stuff haha
@ralph3295
@ralph3295 3 ай бұрын
goat
@punditgi
@punditgi 7 ай бұрын
Nice proof! So, why did you put proof in quotes in the title of the video?
@PrimeNewtons
@PrimeNewtons 7 ай бұрын
Some would say it's not rigorous
@punditgi
@punditgi 7 ай бұрын
@@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! 😃
@franklin-jn2qe
@franklin-jn2qe 4 ай бұрын
Great proof! But I wonder what if f(a)=g(a)=∞? ∞/∞ is also a indeterminate.
@PrimeNewtons
@PrimeNewtons 4 ай бұрын
You do it again
@user-vo2wn4ro8g
@user-vo2wn4ro8g Жыл бұрын
how do u prove the generalized version
@PrimeNewtons
@PrimeNewtons Жыл бұрын
That would be in analysis. Not yet in my scope of videos.
@prithwishsen4710
@prithwishsen4710 Жыл бұрын
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
@PrimeNewtons
@PrimeNewtons Жыл бұрын
Your question is interesting. Please email picture of the written question to me. primenewtons@gmail.com. Or just message me on Instagram.
@prithwishsen4710
@prithwishsen4710 Жыл бұрын
@@PrimeNewtons I don't have Instagram so I mailed it to you
@ClaytonSibara
@ClaytonSibara Ай бұрын
This is so smart, that it worries me 🤣
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