Matinga’s Differential Calculus

Technical Note

Please observe BODMAS sequencing in all examples for the correct results. For the true set of values, tabulate the f (x) result. Graphical plotting generally will not concur as the functions are novel.

Magnitude of x

(1) f (x) = ( x ^ 1/2 ) ^ 2

Orthodox square root of x

(2) f (x) = ( x ^ 2 ) ^ 1/2

Magnitude of x, with upper limit of d/2

(3) f (x) = (d/2) * ( 1 ^ 2 - x ^ 2 ) ^ 1/2

Magnitude of f(x), with lower limit, C, and upper limit of C + d /2, with the scalar upper limit of d/2. Substitute any equation for x. This is simplified differential calculus:

(4) f (x) = C + (d/2) * ( 1 ^ 2 - x ^ 2 ) ^ 1/2 , where c is x [min] and d/2 is x [max].

© Xerqon ABN 97661410108 2025