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Re: Re: A plot of Sign[x]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg94201] Re: [mg94164] Re: A plot of Sign[x]
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Sat, 6 Dec 2008 19:59:24 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <gh8hjr$r0h$1@smc.vnet.net> <ghb5da$rlj$1@smc.vnet.net> <200812061114.GAA16084@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

I'm not sure I see the point of this example. Yes, the function is
continuous at 0, as is evident if, for example, you change the plot
domain to (x,-0.001,0.001}. However, why should that mesh point you
obtain be at such a peculiar position?

If you include the option MaxRecursion->11, say, then that point moves
toward 0. And something like

   Plot[2/(Exp[-10000 x]+1)-1,{x,-1,1},
        MaxRecursion->11,Mesh->All,MeshStyle->{PointSize[.01],Red}]

reveals a bit more about what's happening.

Szabolcs Horv=E1t wrote:

> What do you think about this plot?  Is the position of the point near
> x==0 incorrect?
>
> Plot[2/(Exp[-10000 x] + 1) - 1, {x, -1, 1}, Mesh -> 21,
>   MeshStyle -> {PointSize[.02], Red}]
>
> No, because it's a continuous function, with no jumps at all!

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305



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