Trying to find 2 functions

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Article #140

#140

From: John Nore
Date: Tue, 27 Feb 2007 10:55

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I have two rows of *random* data and for each one of them, I am trying to find a 
corresponding function that matches to this data, if such exist.

The two rows are something like (replacing the values with abstract letters):


Av    Ev
Av-1  Ev-1
.    .
.    .
.    .
A1    E1
A0    E0


What I consider as axioms:

f(Av)< f(Av-1) < ... <f(A1) <f(A0)
g(Ev)< g(Ev-1) < ... <g(E1) <g(E0)

lim f(Av)= 0, lim g(Ev)= 0
v->+inf       v->+inf

(concluded from the above):
f(Ax)= (1/x) * F(Ax)
f(Ex)= (1/x) * G(Ex)

-------------------------------------

 From the above I conclude:

lim f(Av)= 0    }
v->+inf         }
                 } ==>
lim g(Ev)= 0    }
v->+inf         }



==> lim f(Av)= lim g(Ev)= 0
     v->+inf       v->+inf


f(Ax)/g(Ex) = F(Ax)/G(Ex)


Here is my first problem:

lim ( f(Ax)/g(Ex) ) = lim ( F(Ax)/G(Ex) ) ==>
x->+inf               x->+inf


0/0 = lim ( F(Ax)/G(Ex) )
       x->+inf


What does this mean for F(Ax) and G(Ex), that lim F(Ax)= lim G(Ex)= 0?
                                               x->+inf     x->+inf


Is there any way to find the full body of f(x) and g(x), or F(x) and G(x)?

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From: John Nore <jnore@no.spam>
Newsgroups: aus.mathematics
Subject: Trying to find 2 functions
Date: Tue, 27 Feb 2007 12:55:40 +0200
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