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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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