A200115 Decimal expansion of greatest x satisfying 2*x^2 - cos(x) = 4*sin(x).

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

Offset

1,2

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 = 1..10000

Example

least x: -0.22123471685655084592875161456517915661...
greatest x: 1.431778732687231131820591799700558843...

Mathematica

a = 2; b = -1; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.23, -.22}, WorkingPrecision -> 110]
RealDigits[r]  (* A200114 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.43, 1.44}, WorkingPrecision -> 110]
RealDigits[r]  (* A200115 *)

Prog

(PARI) a=2; b=-1; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 29 2018

Crossrefs

Cf. A199949.

Sequence in context: A103552 A127673 A016698 * A332496 A038763 A200384

Adjacent sequences: A200112 A200113 A200114 * A200116 A200117 A200118

Keyword

nonn,cons

Author

Clark Kimberling, Nov 13 2011

Status

approved