<p> Infinitesimal amths ==>> plot Tangent at user [xo, yo] </p>

a0e112fd-4790-4513-9f49-0a830a098cd8 14 15 12 decimal

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

V 20 :

a 50 :

b 100 :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

r a 2^b 2^+ 2 / (12 /^:

ω V r / : 0.253

t 08 0.01 range : k 1 t rows range X k el 501 ω t k el * π 2 / + sin - (* eval : Y k el 100 ω t k el * sin * eval : 21 line for 21 line

x f X Y x linterp :

x c 10 x ≤ (x 84 ≤ (& cases :

M X Y augment :

XY M 400 row (: 23.3815 84.6512 12 mat

assign coordinates of user tangent

M rows 801

xo 23.3815 :

yo 84.6512 :

xy XY + 20 black plot :

<p> Infinitesimal amths ==>> plot Tangent at user [xo, yo] </p>

The function x f x f :

Algo style Memo formula of incremental analysis of this demo example h 0.1 : (increment ≡ x h f deriv 0.5 x h - f x f - x h - (x - / x f x h - f - x x h - (- / + (* : x h f D1 x 2 h * + f - 8 x h + f * + 8 x h - f * - x 2 h * - f + 12 h * / : (1rst Derivative ≡ x h f D2 x 2 h * + f - 16 x h + f * + 30 x f * - 16 x h - f * + x 2 h * - f - 12 h 2^* / : (2nd Derivative ≡ 41 line

x f x c * 10 x h f D1 * 2 1 sys

The curvature x K x h f D2 1 x h f D1 2^+ (32 /^/ :

xo h xo K D1

The normal x N xo h xo K D1 (1 -^x xo - (* - xo K + :

x K x c *

The tangent x T xo h xo K D1 (x xo - (* xo K + :

x λ 10 x ≤ (x 50 ≤ (& cases :

x f x c * x T x λ * yo + xy 3 1 sys

t Clear 1

t x 5050 ω t * π 2 / + sin * - :

t y 100 ω t * sin * :

t c t x t diff t y t 2 diff * (t y t diff t x t 2 diff * (- abs t x t diff (2^t y t diff (2^+ (32 /^/ :

x 0 > ( x 8 < ( & x c not defined if