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From: David C. Ullrich on 17 Jan 2010 06:02 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 |