Maxima (cvs) fails to evaluate some limits arbitrarily

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Surely Richard, if you are using l'Hospital rule for a ratio of f/g where one 
of the functions (f or g) is a polynomial, you could at least think that the 
degree of the said polynomial provides an estimate as to how many times you 
should repeat l'Hospital rule. That would probably be a better guess than 
just "5".

That was my point. I just don't know if it is worth it to implement such an 
algorithm.

I don't doubt you when you say that "simply this expression" is an ill-posed 
problem. Anyhow, for such a thing, the burden of the proof is on the person 
presenting the problem... 

I was, in no way, suggesting that we could know exactly how to evaluate any 
limit using a unique algorithm. That's silly.

> >>And beside, is there an algorithm to know when
> >> you should give up on l'Hospital rule??? I am sure there is... but would
> >> it help?
>
> I doubt there is an algorithm.
> L'hopital's rule is used for forms  inf/inf  0/0  and by various tricks,
> inf-inf .
>
> There is an interplay between taking the derivative of the numerator
> and denominator separately, and then simplifying the ratio.  If the
> simplification process does not work well enough, you do not make
> any headway.  Simplification is not something that can be guaranteed.
> There are a few PhD theses on this topic, most recently I think
> by D. Gruntz.
>
> Here's what I suggest.  If the limit() command ultimately ends up
> without resolving the limit, that a message be constructed of all
> the information collected along the way.
> It might also provide suggestions on how to set various flags
> differently.
> Alternatively, a better program could be written... for all I know,
> l'hopital's rule might not even be needed.   One of the very few
> algorithms you learn in integration ... integration by parts ...
> is not used by Macsyma.
>
> RJF
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