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Math Forum » Discussions » sci.math.* » sci.math.num-analysis.independent

Topic: help..... e^Pi > Pi^e
Replies: 3   Last Post: Oct 4, 2004 4:02 AM

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George Russell

Posts: 157
Registered: 12/6/04
Re: help..... e^Pi > Pi^e
Posted: Oct 4, 2004 4:02 AM
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Uwe Schmitt wrote (snipped):
> I would check f(x) = e^x - x^e for monotony and extrema.

In fact there is a way which uses no calculus. I would advise the original
poster to take
(1) an inequality for e^y (with y > 0), which you can get from the power series;
(2) pi > e.
and try to put the two together.

I don't want to give any more information; I would hate to deprive anyone
of the pleasure of discovering the solution for themselves.

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