A200114 Decimal expansion of least x satisfying 2*x^2 - cos(x) = 4*sin(x), negated.

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

Offset: 0

Author

Clark Kimberling, Nov 13 2011

Keywords

• nonn
• cons

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A199949.

Programs

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 *)

PARI

a=2; b=-1; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 29 2018