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-   -   inequality (http://mymathforum.com/algebra/22079-inequality.html)

JC October 28th, 2011 04:05 PM

inequality
 
Could anybody give some hint how to prove



Thanks in advance.

dibyendu October 29th, 2011 06:39 AM

Re: inequality
 
Note that the inequality holds for

Next, consider the function:




You can easily show that for

This completes the proof.

JC October 29th, 2011 11:40 AM

Re: inequality
 
Thanks. Though you have some mistakes, but first of all I can't understand why the derivative may be something to judge about inequality's correctness.

dibyendu October 29th, 2011 12:50 PM

Re: inequality
 
Quote:

Originally Posted by JC
Thanks. Though you have some [color=#FF0000]mistakes[/color], but first of all I can't understand why the derivative may be something to judge about inequalitys correctness.

Please point out the [color=#FF0000]mistakes[/color].

JC October 29th, 2011 01:18 PM

Re: inequality
 
I think you thought f(x) = 1 / ((x+1) sqrt(x)) - 2tan^(-1) sqrt(x) [color=#FF0000]+[/color] 2tan^(-1) sqrt(x-1).
This gives f'(x) [color=#FF0000]>[/color] 0 for x > 1.

skipjack October 29th, 2011 02:35 PM

Quote:

Originally Posted by dibyendu
This completes the proof.

A slight exaggeration; it's important that

JC October 29th, 2011 04:32 PM

Re:
 
Quote:

Originally Posted by skipjack
A slight exaggeration; it's important that

:D Skipjack, after this comment everything is clear to me now. I solved it and understood.
Many thanks to dibyendu and skipjack.


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