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"
>
> 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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