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Re: Very simple limit, why doesn't it evaluate?

• To: mathgroup at smc.vnet.net
• Subject: [mg31923] Re: [mg31909] Very simple limit, why doesn't it evaluate?
• From: Andrzej Kozlowski <andrzej at bekkoame.ne.jp>
• Date: Wed, 12 Dec 2001 04:14:04 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Computing limits is done by means of a number of ad hoc tricks rather 
than a universal algorithm, so there will always be cases that 
Mathematica can't manage but can be done "by hand". In general when 
Mathematica can't find a limit it is a good idea to load in the 
Calculus`Limit` package and try again. In this case this case we get:

<< Calculus`Limit`

In[2]:=
Limit[4^(3 + n)/(-5 + 3^(4 + n)), n -> Infinity]

Out[2]=
Infinity

This is with Mathematica 4.1 so I am not sure what happens with 3.0 but 
I suspect the same thing.

Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/

On Tuesday, December 11, 2001, at 03:33  PM, Jacek Dziedzic wrote:

> It stunned me that the Mathematica 3.0 returns this very simple limit
> unevaluated:
> 4^(n+3)/(3^(n+4)-5), with n -> infinity.
>
> Moreover, the NLimit function returns 1.0756... which is a rather poor
> approximation of infinity (the expected result)... Well I can understand
> that NLimit is numerical and can't be relied on, but why does the 
> original
> Limit[] die on that? Or am I doing anything wrong?
>
> - Jacek Dziedzic
>
>
>
>
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