A198137 Decimal expansion of greatest x having 2*x^2-4x=-3*cos(x).

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

Offset: 1

Author

Clark Kimberling, Oct 22 2011

Keywords

• nonn
• cons

Comments

See A197737 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: 0.85876971369761442119310432181053308611...
greatest x: 2.4766169740668170810192726417322477...
		

Crossrefs

Cf. A197737.

Programs

Mathematica

a = 2; b = -4; c = -3;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -1, 3}]
r1 = x /. FindRoot[f[x] == g[x], {x, .85, .86}, WorkingPrecision -> 110]
RealDigits[r1] (* A198136 *)
r2 = x /. FindRoot[f[x] == g[x], {x, 2.4, 2.5}, WorkingPrecision -> 110]
RealDigits[r2] (* A198137 *)