Derivate OFa number
- From: "NILS BÖRJESSON" <borje@xxxxxxxxxxxx>
- Date: Mon, 30 Jan 2006 02:04:24 GMT
Now over too something completly different:
If you let the derivate of a number bee
such that D(AB)=D(A).B+D(B).A
AND D(e)=e
then one soloution is:
The number 5 have the derivate 5.ln5
The number 6 have the derivate 6.ln6
ETC.
The number -5 have the derivate -5.ln5
The number -6 have the derivate -6.ln5
ETC.
THEN THE following formula holds:
D(A/B)=(B.D(A)-A.D(B))/B^2
D^n is the function F(A)=D(D(D(...D(A)...))) D, n times
Then it seems that
D^1 D^3 D^5 D^7 ETC. CONVERGE TO=E(A) ON the intervall [-e,e]
AND
D^2 D^4 D^6 D^8 ETC. CONVERGE TO=F(A) ON the intervall [-e,e]
and E(A)=-F(A)
F(A) looks like this:
|
_ __ ____ _______ 1/e|_________ ______ ___ __
|
-e______________________________0_______________________________e______
|
_ __ ____ __________| _______ ___ _
-1/e|
.
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