A200230 Decimal expansion of greatest x satisfying 3*x^2 - 2*cos(x) = sin(x).

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

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: -0.6010846085447445780840915757937924370...
greatest x: 0.83362047030745407827417017871253212...

Mathematica

a = 3; b = -2; c = 1;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.61, -.60}, WorkingPrecision -> 110]
RealDigits[r]   (* A200229 *)
r = x /. FindRoot[f[x] == g[x], {x, .83, .84}, WorkingPrecision -> 110]
RealDigits[r]   (* A200230 *)

Prog

(PARI) a=3; b=-2; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 30 2018

Crossrefs

Cf. A199949.

Sequence in context: A269296 A371502 A334363 * A069995 A199863 A181180

Adjacent sequences: A200227 A200228 A200229 * A200231 A200232 A200233

Keyword

nonn,cons

Author

Clark Kimberling, Nov 14 2011

Status

approved