Re: How to treat this false singular point?

• To: mathgroup at smc.vnet.net
• Subject: [mg68455] Re: How to treat this false singular point?
• From: "simon yang" <yanshanguke at 163.com>
• Date: Sat, 5 Aug 2006 03:47:02 -0400 (EDT)
• References: <eauut9\$14n\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```I had made a mistake again, haha, sorry.
In: Limit[(x-10)*Log[Abs[x-10]],x->10]
Out: 0

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
>
> ---- simon yang <yanshanguke at 163.com> wrote:
> > Dear everyone,
> > I have a function:
> > f[x_]:=(x-x1)Log[Abs[x-x1]] + (x-x2)Log[Abs[x-x2]] + ... +
> > (x-xn)Log[Abs[x-xn]],
> > {x1,x2,...,xn}={100,200,300,...} for instance
> > How to get value: f[x] as there are different singular at different x?
> > I know at x=xn, f[x]==1, But Mathematica return: "Indeterminate", What
> > should I do?
> >  what others do in C++, Fortran ?
> >

```

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