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#1 2012-10-26 20:46:42

Harold
Guest

Inequality with pi and e

What is the solution of this problem?and how is the problem solved-

#2 2012-10-26 21:26:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,417

Re: Inequality with pi and e

Hi Harold;


This one has been around for a long time. The standard answer starts with raising both sides to the power of

after that it is a maxima-minima problem.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2012-10-26 21:47:54

Harold
Guest

Re: Inequality with pi and e

You mean e^e is always bigger than pi^pi?but why?

#4 2012-10-26 21:50:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,417

Re: Inequality with pi and e

Hi;

e^e is not greater than π^π. That is not what I said. You did something wrong with the first step.

From here it is an ugly calculus problem.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2012-10-26 22:31:57

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,092

Re: Inequality with pi and e

Looks to me that y = x^(1/x) has a single maximum at x = e.

See graph and derivative graph.

Bob

View Image: Harold.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#6 2012-10-27 11:47:28

scientia
Member
Registered: 2009-11-13
Posts: 222

Re: Inequality with pi and e

Let
; then
when
. So
is decreasing for
; as
,
, i.e.
.

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