Find f(x) ( JEE ADV 2024) #1

[@Mk3737]

I am a JEE aspirant, and I have been watching your videos for a month. I love your videos and your concepts. Keep it up!!

[@Demogorgan07]

Agar tu jee aspirant hota to ye channel pe kya karta ye koi jee coaching channel nahi hai issliye chaaplusi wale comments na kie karo

[@Mk3737]

@@Demogorgan07 First of all, what do you mean by 'ye channel pe kya karta'? And of course, I know it's not JEE coaching-no need to state the obvious, Sherlock. But is it wrong to watch or follow channels that aren't related to 'JEE coaching'? 😂 Bro, go touch some grass instead of trash-talking in the comment section.

[@Mk3737]

@@Demogorgan07 "First of all, what do you mean by 'ye channel pe kya karta'? And of course, I know it's not JEE coaching-no need to state the obvious, Sherlock. But is it wrong to watch or follow channels that aren't related to 'JEE coaching'? 😂 Bro, go touch some grass instead of trash-talking in the comment section."

[@kunaaaalllll]

​@@Demogorgan07Yeah blud you know everything right?🤓☝🏻

[@Yeah_its_desi]

​​​@@Demogorgan07 I am Jee aspirant too Or mene bhi is channel ko subscribe kia hai Coz I love doing Maths, not just for the sake of marks So ur logic is lame ki Jee walo ko to Jee channel pe hi hona chahiye

[@Notthatkindofdr]

You should not use l'Hopital's rule until you know that f(t) is a differentiable function --- that is, you can't write f'(t) until you know it exists. Apparently the original JEE problem did in fact say that f is continuously differentiable, but you did not mention it here. However, I think you can show that the function is differentiable directly by re-writing the limit expression in the right way.

[@LukieReal]

i’ve only just begun calculus but this doesn’t seem too tricky once you get the hang of differential equations (i could be completely wrong haha) but i love how elegant this all turned out. pretty cool to see such a concise function as the final result too!

[@vectorsahel5420]

It's way harder than it looks lol

[@vishalmishra3046]

At t = x, both numerator and denominator are 0, so fraction can be replaced by a ratio of derivatives of t to get [ 10t^9 f(x) - x^10 f'(t) ] / (9t^8) which is now no longer 0/0. So, 10 x^9 f(x) - x^10 f'(x) = 9x^8. This equation looks so much like (f/g)' = (f' g - f g') / g^2, so let's try g(x) = x^10 to get - [ f(x) / x^10 ]' = [ f'(x) x^10 - 10 x^9 f'(x) ] / x^20 = - ( 9 x^8 ) / x^20 [ substituted the numerator from the above ] = -9 x^-12 Now integrate both sides w.r.t x to get [ f(x)/x^10 ] = -9 x^-11/-11 + c. At x = 1, LHS = f(1)/1^10 = f(1) and RHS = -9/-11 + C = 2, so C = 2 - 9/11 = 13/11 Therefore, f(x) / x^10 = 9/11 x^-11 + 13/11, so f(x) = 9 / (11x) + 13 x^10 / 11 *Simple. Right* ?

[@MaheshKumar-lx1ku]

Great observation 🫡

[@hamazoon.]

5:08 notice how on the left of the equation it is (x^10)’f(x) - x^10f’(x) which is similar to [x^10f(x)]’. All you have to do swap from x -> -x and it will become [x^10f(-x)]’= -9x^8 which is a much easier problem to integrate.

[@joseluishablutzelaceijas928]

Thank you for the problem and its solution. I guess at 4:05 you could also "reconstruct the derivative" by multiplying both sides with -9/x^12 to get that the derivative of f(x)/x^10 is equal to -9/x^12. From here you could simply integrate both sides and then multiply with x^10 to get that f(x) = C*x^10+9/(11*x), which due to the constrain leads to f(x) = (13*x^11+9)/(11*x).

[@رياضياتللمرحلةالمتوسطة]

شكرًا

[@PrimeNewtons]

Thank you 😊

[@Duckallister]

Did this one with t = qx and lim_(q -> 1). The limit changes in a way that makes the definition of the derivative appear (the one from the quantum derivative) and leads to the same ode. Nice problem, I enjoyed it a lot.

[@utuberaj60]

Excellent work Mr Newton in the New Year. I am a fan of yours, more so, as your range of problem-topic is truly humongous. God bless you dear. I also echo the sentiments of many JEE aspirants who loved your explanation.

[@Maths786]

Sir, please do old questions of JEE ADVANCED more because they are tuff!

[@redroach401]

Very elegant problem combining limits, algebra and ODEs. Tha k you very kuch!

[@kateknowles8055]

Thank you. This makes me think I am fifty years younger and back at university again. The difference is that you are here for me if I follow this through as homework! PS I did not do brilliantly at university.

[@Fariq-n2c]

It will be an honour for me, if you make a video from Fourier Transform.

[@FatimaMahdjoub-s6g]

Thanks sir watching you from Algeria❤

[@yashuseerviyt]

your explanation is very understandable

[@AdrianRif]

I wish you’d been my math lecturer at college. You are awesome teacher.

[@drinkup9835]

Can you do videos on Laplace transforms?

[@galand208]

just realised I was the one mistaking something

[@sajalchakraborty9233]

Well done!

[@Shishir27]

What a beautiful question

[@logeshs8905]

Sir i couldn't understand the answer in this 13 th step could you please help me get over it?

[@obeyy0urmaster]

I love the problems with integrating factors !!!!!

[@donmoore7785]

Very nice!

[@lornacy]

Nice, as usual!

[@Maths786]

Nice video sir!❤

[@petelok9969]

Is this a question you would expect more from a differential equations course? When I first seen it I didn't know what to do, I was thinking of parametric equations etc etc I haven't looked at differential equations in a while that's probably why...

[@surendrakverma555]

Thanks Sir

[@criniack]

Continue your integration series please.

[@priyanshsrivastava3571]

Kindly once look upto the questions from ISI CMI

[@suyunbek1399]

Thou art the Prime Newtons, the son of the living Math.

[@rezaghajar6564]

Hello. How come you didn't put a + C when you solved the integral for the integrating factor?

[@nicolascamargo8339]

e^(una función que derivada sea el integrando + constante C) Por propiedades de exponenciales esto es e^(una función que derivada sea el integrando)*e^(constante C) Pero e^C viene a ser otro número que no conocemos y esto es en defecto D obteniendo con simbología: μ=D*e^(una función que derivada sea p(x)) donde la forma original es: y'+p(x)y=q(x). Siguiente paso quedaría D*(1/x¹⁰)*f(x)=Integral de D*(-9/x²)*(1/x¹⁰) dx que por propiedades de la integración al sacar D como contante en ella es lo mismo dividiendo entre D que por cierto es >0 porque es e^C donde la base e elevada a algún número es >0 que resolver: (1/x¹⁰)*f(x)=Integral de (-9/x²)*(1/x¹⁰) dx

[@sckani3432]

Nice, sir. S Chitrai Kani

[@gel2709]

Thanks, but the answer doesn't contain ALL functions f, because you have analized only one-differentiable functions

[@Blingsss]

This video reminded me how satisfying it is to crack a tough JEE problem! Understanding functions requires patience, and resources like SolutionInn have helped me build that step by step. Here’s to conquering JEE Advanced one f(x) at a time.

[@Ebooks_]

Sir do more from this exam I am preparing for this exam it will be useful 😊

[@anas-altaleb]

can we solve it without L'H rule ??!

[@Christopher-e7o]

X,2×+5=8

[@marioguercio8722]

Siempre se ve muy borroso, por lo que es dificultoso seguir el procedimiento. Siempre ocurre lo mismo con tus vídeos.

[@harshplayz31882]

Easy question

[@robertveith6383]

No, it is *not* an "easy" question.

[@saswatasaha9519]

​@@robertveith6383 Yes it's very easy

[@alphazero339]

​@@saswatasaha9519hi I'm sixth grade and it's very easy I solved it under 1 minute

[@anonymoushere7786]

​@@saswatasaha9519ok genius ... It is very easy .

[@fecat6294]

third ngab

[@narangfamily7668]

Fun question. So easy tho

[@robertveith6383]

No, it is *not* "so easy.* It is neither "easy."

[@alphazero339]

​@@robertveith6383hi Im fourth grader and I solved it under 63 seconds easily

[@anonymoushere7786]

​@alphazero339hi I am speaking from my mother's womb ... I agree that it is very easy

[@alphazero339]

@@anonymoushere7786 my brother is in first grade and was also able to solve it but it took him 3 minutes

[@Rednodge_9]

​@alphazero339 i'm speaking from my dad's ball and i can confirm this is solvable in 1 yottasecond

[@YohannesGetu-o3x]

First comment😊

[@alphazero339]

Congratulations😊finally, you've achieved something in your life

[@YohannesGetu-o3x]

​@alphazero339 Yep bro don't worry we are the same;you also achieved what your mother always wished for, replying to me😊

[@alphazero339]

@@YohannesGetu-o3x tell your mom to stop sending me naked pictures or I will block her. It was just one night

[@DarthVader-mp5qp]

Indians acting like this is hard lol... it's normal for us Greeks

[@L0ws-289]

True, but what else do you expect from labourers lol. They all got the cheap labourer mindset.

[@srisaishravan5512]

Retards

[@sajuvasu]

Im indian and this q isnt haard.. Its pretty simple... But the real JEE advanced monsters are still hiding... Thats why jee adv is the 2nd most toughest exam in the world... No hate... But yeh just some facts...

[@asianvlogger176]

Then, give Jee advanced at the age of 17.

[@DarthVader-mp5qp]

@asianvlogger176 I gave Panhellenic examinations in physics, chemistry, and math at the age of 17, me alongside the entirety of the country. If you want, go and check out the exam for physics, it's available online. Type panhellenic examinations 2024. We had 3 hours to complete a 10 page exam, and when the results came in, 60% of all the students in Greece got below 50/100... I got 93 and I must admit it was quite a journey. And that was 1 for 3 subjects. The point is im tired of seeing Indians complain like crybabies that their exam is the hardest, there are many other countries like mine and yours whose system is extremely hard.

[@dieuwer5370]

You're butchering the name of the rule. :) Say it as: "Luh Oh Pee Tahl".

[@shay_playz]

That's incorrect, Guillaume de l'Hôpital (whom this rule was named after) was a French mathematician. 'de l'Hôpital' is actually a title which morphed into his last name. Transliterated, it means "of the hospital". l'Hôpital is read as 'Loh pee tahl' in both French and in English. The 'ô' means that the 'o' vowel should be read without the lowering of the vowel, so the first syllable shouldn't be read as 'low' Basically the L apostrophe doesn't double the way it is phonetically pronounced, instead l'Hôpital is read as one word Lôpital. Since the l' is a determiner, meaning 'the', in French and in English, if it Precedes a consonant sound, then it is read separately as Luh, otherwise it fuses with the vowel sound, in this case the H in Hôpital is always silent in both English and in French, therefore it would be phonetically incorrect to say Luh Oh Pee Tahl. Hope this helps.

[@marioguercio8722]

Siempre se ve muy borroso, por lo que es dificultoso seguir el procedimiento. Siempre ocurre lo mismo con tus vídeos.

[@nicolascamargo8339]

En que parte?