Using roots of g(1-exp(-x)) near x=30, the period is 1.38629436093 vs. 2 log(2) = 1.38629436111. --- "Schroeppel, Richard" <rschroe@sandia.gov> wrote:
1.385 looks suspiciously like 2 log 2 = 1.3862...
Rich
-----Original Message----- From: math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com on behalf of Fred lunnon Sent: Tue 9/12/2006 10:08 AM To: math-fun Subject: Re: [math-fun] mis-defining limits
On 9/12/06, Eugene Salamin <gene_salamin@yahoo.com> wrote:
Plot g(1-exp(-x)). For x > 6, the graph becomes periodic.
g(x) ~ 0.5 + 0.027 sin(2 pi (x - 0.526) /1.385).
Gene
I think maybe the above should have read
g(1-exp(-x)) = 0.5 + 0.027 sin(2 pi (x - 0.526) /1.385)
which does look to be true as x -> 1- with error O(1-x).
All that spiel about g(x) converging on the unit circle is codswallop, because the relation g(x) + g(x^2) = x fails to hold in the limit --- nice one!
If I'd listened to advice and "used a calulator" in the first place, I might have spared myself a very red face here.
WFL
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