Learning that limit is 0 from above



On 10/31/07, Stavros Macrakis <macrakis at alum.mit.edu> wrote:
> > (%i1) f(x) := exp(-x);
> > (%o1)                          f(x) := exp(- x)
> > (%i2) limit(f(x),x,inf);
> > (%o2)                                  0
> > (%i3)
> >
> > In this example, the convergence to zero is from above (0^+). Is it
> > possible to have maxima tell us it?
>
> Yes, compute limit(1/f(x),x,0,plus).  If the result is inf, then the
> original converges from above; if minf, from below.

That is clever! Thanks!

Paul

> By the way, Maxima is generally better at working with expressions than
> functions, so I would have written the above as
>
>     f: exp(-x)$
>     limit(f,x,inf);
>     limit(1/f,x,inf);
>
> Hope this helps,
>
>          -s
>