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Re: limit problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg58929] Re: [mg58910] limit problem
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Sun, 24 Jul 2005 01:21:50 -0400 (EDT)
*References*: <200507230932.FAA29066@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
On 23 Jul 2005, at 11:32, Chris Chiasson wrote:
> Dear MathGroup,
> Honestly, I see no reason why this should return "unevaluated"
> instead of zero.
>
> FullSimplify[Limit[E^(-R t),t\[Rule]Infinity],Infinity>R>0&&Element
> [R,Reals]]
>
> 5.2 on windows
>
> Regards,
> --
> Chris Chiasson
> http://chrischiasson.com/
> 1 (810) 265-3161
>
>
There is no "mathematical" reason of course but there is a
"Mathematica reason". First note that
Limit[E^((-R)*t), t -> Infinity, Assumptions -> R > 0]
0
which is, in fact, the only assumption you need. However, what
happens in your case is that you ask first Mathematica to evaluate
Limit without any assumptions on R. If Mathematica at this point
returned a conditional answer in the form
If[R>0,0,Limit[E^(-R t),t->Infinity]] or something of that kind than
indeed you would have got:
FullSimplify[If[R > 0, 0, Limit[E^(-(R*t)),
t -> Infinity]], Infinity > R > 0 && R â?? Reals]
0
Unfortunately Mathematica returns an unconditional answer (the
original input) and applying FullSimplify with assumptions has no
effect because FullSimplify does not simplify Limits (I think!).
Andrzej Kozlowski
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