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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

• References:
  • limit problem
    • From: Chris Chiasson <chris.chiasson@gmail.com>