Re: Re: Limit with restrictions
- To: mathgroup at smc.vnet.net
- Subject: [mg34324] Re: [mg34304] Re: [mg34269] Limit with restrictions
- From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
- Date: Wed, 15 May 2002 03:35:11 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Tuesday, May 14, 2002, at 05:11 PM, Hannes Egli wrote:
>
> Clear[p]
> p = Simplify[m^(-1 + a + b + n),{a > 0, b > 0, n > 0, a + b + n >1}];
> Needs["Calculus`Limit`"];
> Limit[p, m -> Infinity]
>
> E^(Infinity*Sign[-1 + a + b + n])
>
> Since I assumed that (a+b+n)>1 the sign of (-1+a+b+n) is unambiguously
> positive
> and the equation should converge to infinity.
The assumption you made in Simplify works only inside Simplify and has
no relevance outside it. Moreover, Limit does not accept any
assumptions, or rather it completely ignores them.
I think it is rather pointless to try to use Mathematica to solve
problems which can be done easily by hand. Unfortunately a large number
of questions sent to this list are of this type.
If you really have a hard problem of this type, which means presumably
tha tit is difficult to determine the sign of the exponent, you should
do it as follows.
In[2]:=
Simplify[Sign[(-1+a+b+n)],{a>0,b>0,n>0,a+b+n>1}]
Out[2]=
1
That is enough to answer your question and there is no point at all to
try to force Limit to give you the answer you already know, and which it
was never meant to do. The same really applies to your "more difficult"
problem.
Mathematica can be very useful in helping one to solve problems even
when it can't do them automatically (which really is true of almost any
problem worth trying). If you really have a problem you can't do
yourself you could try sending it here and there is a good chance that
Mathematica will prove helpful. But really, it is very easy to generate
questions of the kind: I can do this easily by hand so why Mathematica's
can't? The best way to answer this sort of thing is to try yourself to
write a Mathematica program that would answer such kind of questions in
sufficient generality. (The method has to be sufficiently general
because there is obviously no point implementing a function that will
solve just one special case. Also, it must be able to solve non-trivial
problems, not just the ones that can be easily done by hand). It is
unlikely that you will succeed but at least it will help you to
understand why it has not been done.