October 28th, 2011, 05:05 PM  #1 
Member Joined: Jun 2008 Posts: 45 Thanks: 0  inequality
Could anybody give some hint how to prove Thanks in advance. 
October 29th, 2011, 07:39 AM  #2 
Senior Member Joined: Aug 2008 Posts: 113 Thanks: 0  Re: inequality
Note that the inequality holds for Next, consider the function: You can easily show that for This completes the proof. 
October 29th, 2011, 12:40 PM  #3 
Member Joined: Jun 2008 Posts: 45 Thanks: 0  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.

October 29th, 2011, 01:50 PM  #4  
Senior Member Joined: Aug 2008 Posts: 113 Thanks: 0  Re: inequality Quote:
 
October 29th, 2011, 02:18 PM  #5 
Member Joined: Jun 2008 Posts: 45 Thanks: 0  Re: inequality
I think you thought f(x) = 1 / ((x+1) sqrt(x))  2tan^(1) sqrt(x) [color=#FF0000]+[/color] 2tan^(1) sqrt(x1). This gives f'(x) [color=#FF0000]>[/color] 0 for x > 1. 
October 29th, 2011, 03:35 PM  #6  
Global Moderator Joined: Dec 2006 Posts: 20,302 Thanks: 1972  Quote:
 
October 29th, 2011, 05:32 PM  #7  
Member Joined: Jun 2008 Posts: 45 Thanks: 0  Re: Quote:
Many thanks to dibyendu and skipjack.  

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