A200299 Decimal expansion of least x satisfying 4*x^2 - 3*cos(x) = sin(x), negated.

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

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: -0.661826141188850993743026123357094...
greatest x: 0.8308503276605474027666209935665...

Mathematica

a = 4; b = -3; c = 1;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.67, -.66}, WorkingPrecision -> 110]
RealDigits[r]   (* A200299 *)
r = x /. FindRoot[f[x] == g[x], {x, .83, .84}, WorkingPrecision -> 110]
RealDigits[r]   (* A200300 *)

Prog

(PARI) a=4; b=-3; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 08 2018

Crossrefs

Cf. A199949.

Sequence in context: A073012 A102522 A201672 * A254134 A194597 A105817

Adjacent sequences: A200296 A200297 A200298 * A200300 A200301 A200302

Keyword

nonn,cons

Author

Clark Kimberling, Nov 15 2011

Status

approved