A200003 Decimal expansion of greatest x satisfying 2*x^2 + cos(x) = 3*sin(x).

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

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=0.75, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

Crossrefs

Cf. A199949.

Sequence in context: A269222 A201994 A243277 * A159590 A309642 A146484

Adjacent sequences: A200000 A200001 A200002 * A200004 A200005 A200006

Keyword

nonn,cons

Author

Clark Kimberling, Nov 12 2011

Status

approved