From: David C. Ullrich on
On Sat, 16 Jan 2010 02:18:23 -0800 (PST), Candide Voltaire
<candideguevara(a)gmail.com> wrote:

>consider the following trivial example:
>lim for x-->0 (x/x)
>applying de L'Hopitals rule gives 1
>However 0/0 can be any number not just 1
>How then can I be sure when I use de L'Hopital for complex expressions
>it wil not hide solutions

Don't know what hidden solutions you're talking about.
First, there's no such tbing as 0/0. Probably you knew that,
and what you meant was

(*) a limit of the form 0/0 can equal anything

or more precisely

(*) if lim f = 0 and lim g = 0 then lim (f/g) can be anything.

That's true. So what? (*) says nothing about the limit of x/x.
When you find that the limit of x/x as x --> 0 is 1 you are
not hiding any solutions - that limit _is_ 1 and nothing else.
(*) does _not_ say that the limit of x/x can be anything
other than 1.

>candide