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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: 97,227

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.

If it ain't broke, fix it until it is.

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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: 97,227

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.

If it ain't broke, fix it until it is.

Online

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,189

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

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

scientia
Member
Registered: 2009-11-13
Posts: 224

Re: Inequality with pi and e

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

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