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#1 2012-10-27 19:46:42

Harold
Guest

Inequality with pi and e

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

#2 2012-10-27 20:26:19

bobbym
Administrator

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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.

#3 2012-10-27 20:47:54

Harold
Guest

Re: Inequality with pi and e

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

#4 2012-10-27 20:50:54

bobbym
Administrator

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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.

#5 2012-10-27 21:31:57

bob bundy
Moderator

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

#6 2012-10-28 10:47:28

scientia
Full Member

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Re: Inequality with pi and e

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

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