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Topic: Probability of success calculation
Replies: 17   Last Post: Jun 2, 2011 2:49 PM

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Brian M. Scott

Posts: 1,259
Registered: 12/6/04
Re: As x approaches 5
Posted: Jun 1, 2011 4:18 PM
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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



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