A198117 Decimal expansion of greatest x having 2*x^2+x=3*cos(x).

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

Offset: 0

Author

Clark Kimberling, Oct 21 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least x: -1.1066958928635031236059456759208208...
greatest x: 0.80159198729974720435776444320005779...
		

Crossrefs

Cf. A197737.

Programs

Mathematica

a = 2; b = 1; c = 3;
f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
Plot[{f[x], g[x]}, {x, -2, 1}]
r1 = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
RealDigits[r1] (* A198116 *)
r2 = x /. FindRoot[f[x] == g[x], {x, .8, .9}, WorkingPrecision -> 110]
RealDigits[r2](* A198117 *)