Meden Agan's latest activity
-
MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.I don't see how that helps either. Let me know if you get anything useful, I'm stuck.
-
MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with
Like.
I found some nice formulas, e.g., with ##y^2=9-16x## we get $$ \dfrac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}=... -
MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.@fresh_42 Did you get something new? If the answer is no, let's go ahead to analyze the solution on MSE.
-
MMeden Agan replied to the thread Prove that ##\lim\limits_{x \to \infty} f(x) = 0##.Mhm, could you outline what's unclear step by step? Hope I can provide a detailed clarification.
-
MMeden Agan reacted to nuuskur's post in the thread Prove that ##\lim\limits_{x \to \infty} f(x) = 0## with Like.
A point to consider is why the function is well defined, i.e, why does the minimum exist for ##x>0##. (If it doesn't then change minimum...
-
MMeden Agan posted the thread Prove that ##\lim\limits_{x \to \infty} f(x) = 0## in Calculus and Beyond Homework Help.Let ##f(x)= \min\limits_{m, n \in \mathbb Z} \left|x- \sqrt{m^2+2 \, n^2}\right|## be the minimum distance between a positive real ##x##...
-
MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.I agree. Your ideas are always excellent, but unfortunately there's nothing we can do. The form in post #86 made me hopeful. But...
-
MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
If we look at the graphic, then we see an almost linear behavior with slope around ##-1## (or so) when we approach ##\alpha=0## and a...
-
MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.Sad. I can't believe that is the only possible solution to the integral.
-
MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
I want to do the Weierstraß substitution now just to see where I end up. However, it doesn't look as if this would help. E.g. $$...
-
MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.Any significant developments? I've come up with a heuristic argument, but I'm becoming more and more convinced that is not correct either.
-
MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
The problem is that we have ##\alpha## and ##p(\operatorname{trig}(\alpha))## in one equation - a dimension conflict. The trick that...
-
MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.IMO, the expression $$2 \int\limits_{0}^{1} \frac{\alpha(z)}{\sqrt{1-z^2}} \, \mathrm dz = \frac{\pi^2}{8}$$ is the best way of...
-
MMeden Agan reacted to fresh_42's post in the thread Prove that the integral is equal to ##\pi^2/8## with Like.
Sure. Ultimately, there is no way to cheat. The problem has to be addressed somewhere. As long as we operate with ##f(\alpha)## and...
-
MMeden Agan replied to the thread Prove that the integral is equal to ##\pi^2/8##.Mhm, but unfortunately that derivative is frankly unmanageable. We seem to have complicated the integral again.