Відео

If you set y(x)=AP and make a y substitution, the integral essentially becomes integral of 1dy from y=l1 to y= l2. Technically with my method you have to split the triangle into 2 right angled triangles ABM and ACM where M is the dropped perpendicular, and integrate over the 2 regions of x left and right of M

Induction is certainly a unique technique for this problem. But that 81/16 is a universal theme across the board for this problem.

Sir love from india i love your methods so much can u pls help in in solving a problem i have a major test on 5 pm today and noone is telling me how to solve this problem pls solve otherwise i will fail 😢😢 🙏🙏 Limit n approaching infinity 1/n.cosπ/n cos2π/n.cos3π/n......cosnπ/n Pls sir pls help me❤😢😢😢😢😢

At 13:33, are you sure it isn’t use r^n, nr^n, n(n-1)r^n, n(n-1)(n-2)r^n as many times as needed? I don’t think the text makes sense as when you differentiate exponents decrease by 1. Could you pls clarify?

Hi sir , I am a student about to enter 2nd year . I am very much Interested in International Mathematics Competition, But i am not fully aware of how to prepare for it ? I couldn’t find much online either . Can you help me sir ? . Is it possible to connect with you on LinkedIn ?

Masterful problem solving... Thanks! I learned a lot from this video.

Plz tell me how can u solved all problam what course are u did it

Hi sir I am 1st year university students I have no experience math competition in high now I'm study in university and I want to solve putnam problam can u recommended me what course and book learn first before the solve putnam question

You didn't proof Os are uncountable, I didn't watch the rest.

Limit questions are beautiful please bring more

This is a typical jee adv question (India)

I believe you can also apply mean value theorem here. C= int|0-b (f(x) dx )/ b.

Nice vids man 👌🏽

Very clear and straightforward demonstration, thanks!

nice

You solve problems like a disciplined chess player. It is nice that you include your steps of thought along with the solution. This channel is a gem.

Nice work sir! Subscribed!

When p is a prime number In gcd(a,b) Can I solve it either a=tp, b=lp??? Gcd(tp,lp)

great method

you said ...we showed there does not exist more solutions ..how???

2:33 why isn't it when n is divisible by 4 ? (Instead of n is divisible by 2) edit : sorry you say it just after : bc a^2+1 isnt divisible by 4.

I see. clever work. 🙌

Please would you solve the problems of RMM 2024? 😊

Nice

How elegant!

Can this problem be solved using Fermat’s Little Theorem?

Nice ❤ problem

An alternative reasoning to the geometric proof: Consider the same argument until 6:36, with no need of H. Create an auxiliary point S = (1,0) and take an angle α of the sector OSQ. By the previous conclusion at 4:12, we have that A_α + B_α = α; and A_(α+θ) + B_(α+θ)= α+θ. Subtract both equations, yielding A_(α+θ) - A_α + B_(α+θ) - B_α = θ. Now, doing a simple drawing of the regions of the equation, we easily conclude: A_(α+θ) - A_α = A_θ, B_(α+θ) - B_α = B_θ. Bring that up to the equation, resulting in A_θ + B_θ = θ, which is what we wanted to prove.

i came up with a completely different solution to this problem. at first the i noticed the f(x+y)=f(x)+f(y). since this is independent of position of arc. take a small angular element dx of the arc and find f(dx)=(dx(cosx))cosx+(dx(sinx))sinx=dx now we just have to add up all the small angles dx

I'm a 12th grader of India I don't know much about putnam examination, it is definetly hard but this question was not too complicated I was able to solve most it in my mind just from the thumbnail... And also your explaination was quick and simple😊

I feel so smart because Squidward teaches me math.

Thanks for posting again.... please do the last two problems (9 and 10) of IMC 2023.

Nice problem.I have only one question.How can I think about ln to solve this problem,or just because the expression is dealing with powers?

Sir please upload more problems

i have two pieces of advice: (1) don't skip too many steps; some steps are not as obvious for typical people and you should keep them in your demonstration (2) explain briefly the logic/thinking of this Cauchy Induction

how did we get derivative when 2 does not divide n

always just 1 :)

Hello and thank you for the great explanation! I have just one question - at 24:06, what is the formula you use to calculate limit of v mk using the limit of u mk?

Superb sir 👌

not even national level last 2 or 3 questions in most countries.

hey i have a doubt! in 4:24 , while writing the expression for Sn+1 in terms of union , we have A belongs to Sn right? but Sn also has many other elements , so what about their union with {Xk} ?

I think in 9:30 the ineaquality should be a<b<a+ε right?

Titu generalizes this to the case in which positive even integer k is in place of 1987. The number of such function is k!/(½k)!, so there are no such functions for odd k

is this the problem where you pick median point to minimize total distance

What if u don't do p=|p|?

very good video!