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Mathematical Question
From: |
Henry F. Mollet |
Subject: |
Mathematical Question |
Date: |
Mon, 02 Aug 2004 13:20:29 -0700 |
User-agent: |
Microsoft-Entourage/10.1.1.2418 |
I have nowhere else to turn, I'm hoping the octave help
list can provide a tip. Many thanks, Henry
y = x/(1-x) - cx^c/(1-x^c),
where c is a positive integer constant
I need to know y in the limit as x approaches 1.
I even have the result by biological reasoning
and it is (c-1)/2 but how do I prove it mathematically?
For example using x = 0.999 and c = 100 we have:
y = 999 - 950.4 = 48.6 whereas (c-1)/2 = 49.5;
Using x = 0.9999 and same c = 100, we have:
y = 9999 - 9949.6 = 49.4 whereas (c-1)/2 = 49.5, close enough.
Somehow I have to expand the second term in the
expression into a series where the first term of the
series will be the same as the first term of the
expression (i.e. x/(1-x)) and they will cancel out.
In my application, the constant c is a positive integer,
and that's what I used for empirical checks of the result
but I have not checked if that's a requirement.
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-------------------------------------------------------------
- Mathematical Question,
Henry F. Mollet <=