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MathGroup Archive 1997

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Re: Re: weird Log[0] *0 result

  • To: mathgroup at smc.vnet.net
  • Subject: [mg9111] Re: [mg9076] Re: [mg9022] weird Log[0] *0 result
  • From: seanross at worldnet.att.net
  • Date: Mon, 13 Oct 1997 23:33:24 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Olivier Gerard wrote:
> 
> Dear Patrick,
> 
> In my recent answer to you I forgot to give you an
> example of a limit involving x Log[f(x)] for which
> the result is not 0.
> 
> Here it is, presented with Mathematica :
> 
> In[1]:= Limit[ x^(1/x), x->0]
> Out[1]= 0
> 
> In[2]:= Limit[ x Log[x^(1/x)], x->0]
> Out[2]= -Infinity
> 
> Hope it helps,
> 
> Olivier
> 
> At 06:05 +0200 97.10.08, Patrick Tao wrote:
> > Hello mma users,
> >
> > I have a quick question on the following computation:
> >
> > the natural log of 0 times 0 writen Log[0]*0
> >
> >
> >
> > Should that not be 0 ?
> >
> > mma is returning an Indeterminate result
> >
> > Can somebody please help me understand this computation.
> >
> >
> >
> > Many Thanks
> >
> > -patrick


The whole thing about indeterminate forms is that they are, in fact,
indeterminate and that you can't tell what their limit is going to be by
casually looking at them.  If you are doing it by hand, you do algebraic
manipulation and then application of L'Hopitals rule.  

A quick way to check mathematicas result it to plot the function for
small x as in:

Plot[x Log[x^(1/x)],{x,1,10^-6}]

This plot shows that the correct answer is, indeed, - Infinity as x
approaches zero from the right.


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