<p> hatch </p>

6912a6ab-8f49-4172-b601-c35a816d497e 42 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

<p> hatch </p>

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und 
g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*N vertical lines (hatching) 
between functions f(x) and g(x) in x-range from x1 to x2 f g x.1 x.2 N hatch dx x.2 x.1 - N / (: h x.1 x.1 f x.1 x.1 g 22 mat : x x.1 x.2 dx - x.1 dx + range h h x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for h 41 line :

Graphing the Analytics of a function

The function a x f a x 3^* :

The curvature a x K a x f x 2 diff 1 a x f x diff (2^+ (32 /^/ :

The normal a x N a xo K xo diff (1 -^x xo - (* - a xo K + :

The tangent a x T a xo K xo diff (x xo - (* a xo K + :

a 0.5 : (user parameter ≡ xo 0.45 - : (point of normalcy ≡ 21 line

x f a x K :

x g a x N :

X a u N u 2 - 0 solve : T a u T u 01 solve : 21 mat

X T 21 mat 1.9828 - 0.4625 21 mat

a 0 N a 0 T 21 mat 1.5298 - 0.5994 - 21 mat

a x K a x N a x T xo a xo K . 15 black 1 5 mat a x f x f x g xo X 20 hatch 6 1 sys

Notes:

1. This document is demo about tangent/normal.

2. Normalcy xo is user.

3. There is a way to determine normalcy xo such

that [f(a,x), K(a,x), T(a,x)] join @ same point.

Not aware of such application ...

Solution is given below.

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Intersection of "normal/tangent" with curvature a u N a u K - 0 ≡ u 2 - 0 solve a u T a u K - 0 ≡ u 1 - 1.5 solve 21 mat 1.943 - 0.7913 - 0.45 - 31 mat 0.45 - 0.45 - 0.9391 31 mat 21 mat

Solving for the triplet junction

jonction of "f & K" is unique fK a u f a u K - 0 ≡ u 0.95 1.05 solve : 1.0039

curvature @ 'fK' a fK K 0.505819995750424

determine a soling intersection a fK Φ 0.505819995750424 :

The tangent @ xo a xo x T a xo K xo diff (x xo - (* a xo K + :

normalcy of the triplet a xo fK T a fK Φ - xo 0.47 - 0.45 - solve 0.4607 -