A199967 Decimal expansion of least x satisfying 2*x^2 + cos(x) = 3*sin(x).

4, 5, 0, 4, 1, 2, 2, 3, 6, 3, 8, 3, 2, 4, 9, 1, 3, 3, 7, 6, 4, 7, 8, 1, 9, 0, 7, 8, 3, 8, 3, 9, 7, 7, 8, 4, 1, 7, 1, 6, 1, 9, 0, 7, 4, 6, 3, 2, 2, 9, 7, 3, 5, 9, 9, 9, 4, 0, 9, 3, 4, 8, 3, 9, 5, 8, 0, 6, 3, 6, 2, 8, 3, 9, 7, 8, 0, 8, 5, 2, 8, 5, 8, 6, 5, 1, 7, 2, 8, 8, 8, 2, 1, 7, 7, 4, 9, 0, 2

Offset

0,1

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Example

least x:  0.45041223638324913376478190783839778...
greatest x: 0.989450014493949167489788332695714...

Mathematica

a = 2; b = 1; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -.1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199967 *)
r = x /. FindRoot[f[x] == g[x], {x, .98, .99}, WorkingPrecision -> 110]
RealDigits[r]  (* A200003 *)

Prog

(PARI) a=2; b=1; c=3; solve(x=0, .5, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

Crossrefs

Cf. A199949.

Sequence in context: A353450 A087492 A366362 * A021226 A197584 A213440

Adjacent sequences: A199964 A199965 A199966 * A199968 A199969 A199970

Keyword

nonn,cons

Author

Clark Kimberling, Nov 12 2011

Extensions

A-number corrected by Jaroslav Krizek, Nov 27 2011

Status

approved