I have deleted my old question about uniform convergence because I dont want to distract people with my old doubts. Now I have the complete proof of it, Its Right that there is uniform convergence however it isnt easy to verify it. Thanks for all!!
I just had a question about the rigor of the argument. The textbook theorem only provides for the existence of limits on the interval for x of (1, inf). Does that not mean it does not follow that the limit replacement method and limit as x -> 0+ has no guarantee to exist? Or is this a reversed flow; the existence of the limit on that interval justifying the substitution? That was the only part that was tough to follow for me. Thanks in advance for any assistance you can provide.
Note that we made a substitution from x to 1/x, so our function AFTER the substitution takes value of x in the interval (0, 1). Thus, taking the limit as x -> 0+ after the substitution is justified.
@@LetsSolveMathProblems Do you not agree no one would have thought of this solution if they hadn't seen this theorem or these limits before?? Thanks for sharing and in advance for answering.
I’m just about to start upper level math. Taking real analysis and abstract algebra this semester. How long before I master problems like these? Is this grad level math or undergrad level? I’m scared I’ll never get to this level...
@@aswinibanerjee6261 I have used the cotagent summation representation, getting S=2+(pi/5)cotg(pi/5). Pi/5= 36°. Expanding cotg(36°) you get S= (800+pi*sqrt(5000-1000*sqrt(5))+pi*sqrt(200-40*sqrt(5))+pi*sqrt(4000-800*sqrt(5)))/400
Does f subscriptt,n mean a function that takes vues n but does NOT mean a function of n, is that correct? Only f(n) means,something is a function of n,correct?
The limit of a product equals,the product,of the limits so x times lnx limit is zero? Why not just do it that way..you get zero times one which is zero ..
I have deleted my old question about uniform convergence because I dont want to distract people with my old doubts. Now I have the complete proof of it, Its Right that there is uniform convergence however it isnt easy to verify it.
Thanks for all!!
That was very informative. Thank you very much.
⭐️
I just had a question about the rigor of the argument. The textbook theorem only provides for the existence of limits on the interval for x of (1, inf). Does that not mean it does not follow that the limit replacement method and limit as x -> 0+ has no guarantee to exist? Or is this a reversed flow; the existence of the limit on that interval justifying the substitution? That was the only part that was tough to follow for me. Thanks in advance for any assistance you can provide.
Note that we made a substitution from x to 1/x, so our function AFTER the substitution takes value of x in the interval (0, 1). Thus, taking the limit as x -> 0+ after the substitution is justified.
@@LetsSolveMathProblems ah of course it inverts the interval. Thank you! This was truly a brilliant solution to watch.
@@LetsSolveMathProblems Do you not agree no one would have thought of this solution if they hadn't seen this theorem or these limits before?? Thanks for sharing and in advance for answering.
What's the drawing software you use?
I’m just about to start upper level math. Taking real analysis and abstract algebra this semester. How long before I master problems like these? Is this grad level math or undergrad level? I’m scared I’ll never get to this level...
Here’s an infinite series suggestion:
S=1-(1/4)+(1/6)-(1/9)+(1/11)-(1/14)+...
The answer is integration of (1-x³)/(1-x⁵) from 0 to 1
@@aswinibanerjee6261 I have used the cotagent summation representation, getting S=2+(pi/5)cotg(pi/5). Pi/5= 36°. Expanding cotg(36°) you get S=
(800+pi*sqrt(5000-1000*sqrt(5))+pi*sqrt(200-40*sqrt(5))+pi*sqrt(4000-800*sqrt(5)))/400
It's pretty easy, you get
S=
(800+pi*sqrt(5000-1000*sqrt(5))+pi*sqrt(200-40*sqrt(5))+pi*sqrt(4000-800*sqrt(5)))/400
Great problem but how can we assume fn(x) to be uniformly convergent?
That's beautiful piecewise quadrature.
I believe that I used the same Idea(But wasn't able to write it properly due to poor internet connection and my old phone)...
Sure thing, Fermat 2.0
区分求積法は便利ですね
But who WHO would ever think of doing that step at 6:00..can you please respond and tell me?
A very inteligent guy
@@arthurgames9610 i am and I didn't
@@leif1075 A very very inteligent guy
@@arthurgames9610 i am am and i didnt...must be dumb luck
maybe ur not as smart as u think then
very easy my friends
혹시 한국인이세요...?
씨발
Much easer with abel summation...
Abel summation is for series... the sequence on the video isnt a series so... ¿can you detail your answer?
Does f subscriptt,n mean a function that takes vues n but does NOT mean a function of n, is that correct? Only f(n) means,something is a function of n,correct?
wat
The limit of a product equals,the product,of the limits so x times lnx limit is zero? Why not just do it that way..you get zero times one which is zero ..