- #1

jostpuur

- 2,116

- 19

[tex]

\frac{x}{\frac{1}{a} + \frac{x}{b}} \;<\; \frac{2b}{\pi}\arctan\Big(\frac{\pi a}{2b}x\Big),\quad\quad\forall\; a,b,x>0

[/tex]

First I thought that if this is incorrect, then it would be a simple thing to find a numerical point that proves it, and also that if this is correct, then it would be a simple thing to prove this via some derivatives or integrals. For some reason I didn't succeed in either objective, and now I'm not sure why I feel confused about this.