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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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