How would one show that e^pi is greater than pi^e without using a calculator?

meghatronic · 12 May 2007 at 02:12

jezsoup said:
Why do they say you cant apply to both?

Elitism bullship.

Arcade Fire · 12 May 2007 at 08:29

If you could apply to both, then everybody would. Oxford and Cambridge both already get far more applicants than they have places, and they're already turning away candidates who could probably handle the difficulty of the course. There's no sense in doubling their workload for no return.

Calder · 12 May 2007 at 08:45

Stiff_Cookie said:
Maybe im just at that level but cant you just replace 'e' with any number?

e = exponential, it's a constant.

Amleto · 12 May 2007 at 10:58

Calder said:
e = exponential, it's a constant.

I beg to differ

Calder · 12 May 2007 at 11:16

Amleto said:
I beg to differ

Wiki said:
The exact reasons for the use of the letter e are unknown, but it may be because it is the first letter of the word exponential. Another possibility is that Euler used it because it was the first vowel after a, which he was already using for another number, but his reason for using vowels is unknown. It is unlikely that Euler chose the letter because it is his last initial, since he was a very modest man, and tried to give proper credit to the work of others.

The exponential function is f(x) = e^x.

Amleto · 12 May 2007 at 11:20

I was just being a pedant