
Re: As x approaches 5
Posted:
Jun 1, 2011 4:18 PM


On Wed, 01 Jun 2011 12:35:03 0700, Alexandros Bantis <ambantis@gmail.com> wrote in <news:94nij9F5phU1@mid.individual.net> in alt.math.undergrad:
[...]
> I'm curious. How is it possible that the function changes > a fundamental property [f(5) == undefined versus f(5) = > 1/6] when all I've done is multiply by 1. I see that > this has happened, but intuitively it feels odd.
It didn't change when you multiplied by 1: the change occurred when you cancelled x  5. After the multiplication by 1 you actually had
(x  5) / [(x  5) sqrt(x + 4) + 3],
which is exactly equal to f and in particular undefined at x = 5. In other words,
f(x) = (1 / [sqrt(x + 4) + 3]) [(x  5) / (x  5)],
but this is equal to 1 / [sqrt(x + 4) + 3] only where (x  5) / (x  5) = 1, i.e., where it's actually defined.
Brian

