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MathGroup Archive 2006

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Re: Limit Question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66458] Re: Limit Question
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
  • Date: Sun, 14 May 2006 02:57:35 -0400 (EDT)
  • References: <e43vun$90e$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Blimbaum, Jerry CIV NSWC PC" <jerry.blimbaum at navy.mil> wrote:
> Why do these give no output?
>
> Simplify[Limit[Exp[-a t],t->Infinity],a>0]
>
> and  same for
>
> Simplify[Limit[Exp[a t],t->Infinity],a<0]

I must guess that it's because:

1. Limit[Exp[a t],t->Infinity] itself cannot be evaluated since the sign
of a is not known.

and

2. Simplify doesn't manage to get the necessary information about the sign
of a inside Limit.

In any event, here's an alternative that does work:

In[10]:= Assuming[a>0, Limit[Exp[-a t], t->Infinity]]

Out[10]= 0

In[11]:= Assuming[a<0, Limit[Exp[a t], t->Infinity]]

Out[11]= 0

Apparently, Assuming does manage to get the necessary information about the
sign of a inside Limit.

Regards,
David


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