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MathGroup Archive 2006

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Re: How to treat this false singular point?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68452] Re: How to treat this false singular point?
  • From: "simon yang" <yanshanguke at 163.com>
  • Date: Sat, 5 Aug 2006 03:46:57 -0400 (EDT)
  • References: <eauut9$14n$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Bob Hanlon wrote:
> f[x_, xList_List] := Total[(x-xList)*Log[Abs[x-xList]]];
>
> f[x, {x1, x2, x3}]
>
> (x - x1)*Log[Abs[x - x1]] + (x - x2)*Log[Abs[x - x2]] + (x - x3)*Log[Abs[x - x3]]
>
> a singularity will exist for each value of x in xList; therefor, f[xn, xList] cannot have the value 1
>
> f[5. - 10^-15, Range[5]]
>
> 10.2273
>
> Plot[f[x,Range[5]],{x,-1,5}];
>
>
> Bob Hanlon

Sorry, I had made a mistake, I mean the limit of (x-xn)Log[x-xn]==1
when x->xn and x>xn.
The f[x] is a part of another function g[x], Mathematica didn't get
this value when met x=xn which I thought it should.


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