Re: Limit Question

• To: mathgroup at smc.vnet.net
• Subject: [mg66456] Re: [mg66452] Limit Question
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 14 May 2006 02:57:30 -0400 (EDT)
• References: <200605130642.CAA08939@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 13 May 2006, at 15:42, Blimbaum, Jerry CIV NSWC PC 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]
>
> thanks...
>
> Jerry Blimbaum
>
>
>

Simplify will not help with Limit problems but Assumptions will:

Limit[Exp[(-a)*t], t -> Infinity, Assumptions -> a > 0]

0

Limit[Exp[(-a)*t], t -> Infinity, Assumptions -> a < 0]

Infinity

The problem is that while Limit now accepts assumptions, unlike other
functions that do so it does not (yet?)  return conditional answers.
Compare this with:

Integrate[E^(-(a*t)), {t, 0, Infinity}]

If[Re[a] > 0, 1/a, Integrate[E^((-a)*t), {t, 0, Infinity},
Assumptions -> Re[a] <= 0]]

Simplify[%, a > 0]

1/a

The only reason why Simplify worked below was that the answer to the
previous output was returned in the form of a condition.

Andrzej Kozlowski

```

• References:
• Limit Question
• From: "Blimbaum, Jerry CIV NSWC PC" <jerry.blimbaum@navy.mil>
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