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Re: Limit Question


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


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