A200231 Decimal expansion of least x satisfying 3*x^2-2*cos(x)=2*sin(x).

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

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: -0.508066683701868134653059484203509821...
greatest x: 0.9632913766196791046556418296641642...

Mathematica

a = 3; b = -2; c = 2;
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, -.51, -.50}, WorkingPrecision -> 110]
RealDigits[r]   (* A200231 *)
r = x /. FindRoot[f[x] == g[x], {x, .96, .97}, WorkingPrecision -> 110]
RealDigits[r]   (* A200232 *)

Prog

(PARI) a=3; b=-2; c=2; solve(x=-.51, -.50, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

Crossrefs

Cf. A199949.

Sequence in context: A343071 A215892 A200643 * A124914 A199376 A011510

Adjacent sequences: A200228 A200229 A200230 * A200232 A200233 A200234

Keyword

nonn,cons

Author

Clark Kimberling, Nov 14 2011

Status

approved