3e650888-b9c7-43d9-a95f-4cecda51edb0 12 4 5 decimal

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

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 :

x f 1 x / :

x g 0 :

b 3 :

Classroom hatch demo ln(x)

x f x g x f x g 1 b 10 hatch 3 1 sys

x f x 1 b int 1.098612

b ln 1.098612

Graphing the Analytics of a function

a x f a x 3^* : the function ≡

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

a x K 6 x * a * 19 x 4^* a 2^* + 2 nthroot 3^/

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

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

Equal distances in both X, Y directions is implicit N(a,x) cutting both axes @ 45 °

a 0.5 : user parameter ≡ xo 0.4732852 - : point of normalcy ≡ 21 line

X a u N u 2 - 1.5 - solve :

x f a x K :

x g a x N :

X 1.682665 -

a 0 N 1.682666 -

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

X a 0 N - 1.427288 106 -^*

a 0 T 0.736096 -

T a u T u 0.5 1 solve :

T 0.736096