<p> X(Φ,a,b,ε) ..... V(x </p>

4c2d6cdc-7241-4f39-925d-a0456c6e0c52 7 4 5 decimal

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

'roots' ... 'solve' NOT responding. 1. 'Division by zero' rare case, maybe unique demo. 2. 'x Not Defined' very common built-in functions. 3. 'Diff(■,■) Not defined' ... most common splines.

"RootSecant" intersect ... descending ▼ convergents Φ a b ε X u 1 el ε : u 2 el b b Φ a b - (* a Φ b Φ - / - : i 2 : u i 1 + el u i el u i el Φ u i 1 - el u i el - (* u i 1 - el Φ u i el Φ - / - : u i el u i 1 - el - abs ε > u i 1 + el u i el u i el Φ u i 1 - el u i el - (* u i 1 - el Φ u i el Φ - / - : i i 1 + : 21 line while u 61 line :

algo style divide by zero detect x V k 1 : j 1 x rows range x j el Vf v f IsDefined 1 ≡ Y k el x k el Vf v f : k k 1 + : 21 line jump end if break try for 21 line Y 21 line :

x Vf v f 12 x * g * v 2^/ - exp - sqrt atanh v 2^* g Vf * / :

g 9.8066 :

Vf 20 : v 1.25 : 12 mat

x Vf v f

x 03 0.001 range :

U x V :

U rows 2808

x x 1 U rows range el :

data x U augment :

XY data data rows row : 2.807 0.1403 12 mat

2.8 Vf v f 0.1403

data XY 1 1 el XY 1 2 el + 150 red 1 5 mat 2 1 sys x Vf v f

click to see 'Division by zero' π Vf v f #

e Vf v f 0.1403

x Clear 1

Infinite  limit x f x 0.5 1 -^x - exp * :

x ∫ π sqrt x sqrt erf * :

x f x ∫ - x 0.35 roots #

x f x ∫ 0.3845 1.098 + 40 black 1 5 mat 3 1 sys

x f x ∫ - x 0.375 0.4 solve #

erf(sqrt(x)) NOT scalar wrt 'x' Not differentiable for 'roots'. error message 'x not defined'.

QED 'f(x) scalar' x f 0.5 - x 0.25 roots 0.8029

QED  '∫(x) NOT scalar' x ∫ 0.5 - x 0.25 roots #

x Φ x f x ∫ - eval :

Intersect Φ 0.375 0.4 1015 -^X :

Intersect 11015 -^* 0.384721988451402 0.384721988440634 0.384477586672068 0.384477669265326 0.38447766923179 0.384477669231788 0.384477669231791 0.384477669231793 0.384477669231793 101 mat

vx 12331 mat : vy 01031 mat : 12 mat

x S vx vy x cinterp :

x λine x 2 - :

x S x λine 2 1 sys

click to see error x S x λine - x 2 roots #

x Φ x S x λine - eval :

Sλ Φ 2.5 2.75 1015 -^X :

Sλ 11015 -^* 2.61111111111111 2.57142857142858 2.61818181818182 2.61803084223014 2.61803398854188 2.6180339887499 2.61803398874987 2.61803398874989 2.61803398874989 2.6180339887499 2.6180339887499 121 mat

jmG: 20230420