Re: A function shaped like...
- From: Paul Abbott <paul@xxxxxxxxxxxxxxxxxx>
- Date: Sun, 03 Sep 2006 22:50:32 +0800
In article <MPG.1f5c100eb51e2eae9896de@xxxxxxxxxxxxxxxx>,
Chris Smith <cdsmith@xxxxxxx> wrote:
I'm looking for an easily computable function for which all of the
following are true:
1. The function is differentiable and monotonically increasing over all
real numbers.
2. f(0) = 1/2
3. lim[x -> oo] f(x) = 1
4. lim[x -> -oo] f(x) = 0
In addition to basic arithmetic, I can use forward trig functions and
square roots.
I assume that you can use exponentials? If so, then
Exp[c x]/(1 + Exp[c x])
for any c > 0 satisfies all your conditions.
Cheers,
Paul
_______________________________________________________________________
Paul Abbott Phone: 61 8 6488 2734
School of Physics, M013 Fax: +61 8 6488 1014
The University of Western Australia (CRICOS Provider No 00126G)
AUSTRALIA http://physics.uwa.edu.au/~paul
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