Re: A function shaped like...

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 could do this easily with an arc tangent, but that's
not available. Thanks for any suggestions.

Hint: Think a bit about x^3/(1 + sqrt(x^6)).
.

Relevant Pages

  • Re: A function shaped like...
    ... "Ignacio Larrosa Cañestro" ... Chris Smith wrote: ... The function is differentiable and monotonically increasing over ... I could do this easily with an arc tangent, ...
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  • Re: A function shaped like...
    ... Chris Smith wrote: ... The function is differentiable and monotonically increasing over all ... square roots. ... I could do this easily with an arc tangent, ...
    (sci.math)
  • A function shaped like...
    ... I'm looking for an easily computable function for which all of the ... The function is differentiable and monotonically increasing over all ... I could do this easily with an arc tangent, ... Chris Smith ...
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  • Re: A function shaped like...
    ... Chris Smith wrote: ... The function is differentiable and monotonically increasing over all real numbers. ... BTW, Virgil's example, viz., ... Math Tutor on the Internet and in Central New Jersey and Manhattan ...
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  • Re: A function shaped like...
    ... Chris Smith wrote: ... The function is differentiable and monotonically increasing over ... Best regards, ... Ignacio Larrosa Cañestro ...
    (sci.math)
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