Re: 97-TEACHING TRUE MATHEMATICS, AP seeks the super easiest calculus p
From
Archimedes Plutonium@21:1/5 to
All on Sun Sep 3 01:58:36 2023
Now I need to add more to the Power Rules of Calculus as we make Polynomials be the only valid functions of mathematics. If you come to math with a function not a polynomial, you are sent home to convert your silly contraption into a polynomial over a
interval in 1st Quadrant Only, a interval of concern.
But in all the years I did calculus, I seem to not have registered in my mind the geometrical significance of the Power Rules. What is the geometry of taking x^2 to the power rule of n(x^n-1) for derivative. Then what is the geometry significance of
taking the integral power rule-- (1/(n+1)) (x^(n+1)).
It seems to me that at one moment in time, that geometry stuck to my mind, but is now elusive, I cannot recall the geometry significance of either Power Rule when played out on x^n.
Cavalieri 1598-1647
So that if we start with a polynomial function such as x^2 -> Y, we instantly know from the power rules that the derivative is 2x and the integral is 1/3x^3.
Derivative Power Rule of a polynomial x^n that the derivative is n(x^n-1).
The Integral Power Rule is sort of the opposite of the derivative rule so for polynomial x^n that the integral is (1/(n+1)) (x^(n+1)).
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)