## Calculus problems please?

Post any maths and/or physics related questions here.

Moderators: Darobat, RecursiveS, Dante Shamest, Bugdude, Wizard

Jetru wrote:I know that one(e^pi or pi^e).
e^pi can be written as e^pi*e/e
pi^e can be written as pi^e*pi/pi
Now thats in the form x^k/x.
Differentiate x^1/x and find maxima, which turns out to be at e.
So e^pi is greater.
That's a popular one.

Yeah, you seem to have seen it before, but you got the details wrong.

The function that has a maximum at e is log(x)/x. So
log(e)/e > log(pi)/pi
log(e)*pi > log(pi)*e
log(e^pi) > log(pi^e)
e^pi > pi^e

Alvaro
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Location: NY, USA

No...i said x^(1/x) has a max at e. I just graphed it. I don't know your technique, but this one works too.

You can't conquer the game if you can't conquer yourself.

Jetru

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Joined: Sat Oct 18, 2003 11:46 pm
Location: Bangalore,India

Jetru wrote:No...i said x^(1/x) has a max at e. I just graphed it. I don't know your technique, but this one works too.

Oh, ok. It was the lack of parenthesis that confused me. My function is just log of your function. It's the same solution in essence.

Alvaro
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Posts: 5185
Joined: Mon Sep 22, 2003 4:57 pm
Location: NY, USA

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