Andrey G. Grozin <A.G.Grozin <at> inp.nsk.su> writes:
>
> On Wed, 20 Dec 2006, miguel lopez wrote:
> > I know that you know, but anyway, if someone care, recall: f equivalent to g
> > when lim f/g = 1
> No it is not, in f/g-1. With your rules,
> limit((sin(x)-x)/x^3,x,0)
> would produce 0
>
> Andrey
>
sin(x) - x is not a product.
Here you take the first NON ZERO taylor polynomial:
(x - x^3/3 - .. )- x = - x^3 /3.
The replacement rule is only for products (and quotients) and powers.
It's not correct do do sin(x) - x = x-x = 0.