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MathGroup Archive 2005

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Re: Re: limit problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58950] Re: [mg58944] Re: limit problem
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 25 Jul 2005 01:12:07 -0400 (EDT)
  • References: <dbt3lm$sk4$1@smc.vnet.net> <42E2A56C.3050808@gmail.com> <200507240522.BAA14483@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I do not think there is any need for this. If Limit returned a  
conditional answer in the manner of Integrate with symbolic  
integration limits, then this problem would not arise. As it is,  
since Simplify and FullSimplify  evaluate their arguments what you  
would get with your suggested approach is a double attempted  
evaluation of Limit, first without the assumptions of Simplify and  
then again with the assumptions: hardly the most efficient way to go  
about this.

Since Integrate already returns conditional solutions applying  
Simplify will normally work the way you expect:



Simplify[Integrate[1/x, {x, a, b}], 0 < a < b]

Log[b/a]

There was no "passing of assumptions" involved and none is needed.



Andrzej Kozlowski

On 24 Jul 2005, at 07:22, Chris Chiasson wrote:

> As others have kindly demonstrated, Assuming is able to pass its
> assumptions to Limit. I know that the second argument of Simplify and
> FullSimplify is for assumptions. For this reason, I think WRI should
> update FullSimplify and Simplify to pass their assumptions to Limit
> and Integrate, etc. Is there a reason why they should not do so?
>
> On 7/23/05, Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com> wrote:
>
>> 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,
>>>
>> Hi Chris,
>>
>> The following works:
>>
>> In[1]:=
>> Limit[E^(-t), t -> Infinity]
>>
>> Out[1]=
>> 0
>>
>> In[2]:=
>> Limit[E^((-R)*t), t -> Infinity]
>>
>> Out[2]=
>> Limit[E^((-R)*t), t -> Infinity]
>>
>> In[3]:=
>> Assuming[R > 0, Limit[E^((-R)*t), t -> Infinity]]
>>
>> Out[3]=
>> 0
>>
>> Best regards,
>> /J.M.
>>
>>
>
>
> -- 
> Chris Chiasson
> http://chrischiasson.com/
> 1 (810) 265-3161
>
>


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