A199184 Decimal expansion of least x satisfying x^2+3*x*cos(x)=2.

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

Offset: 1

Author

Clark Kimberling, Nov 04 2011

Keywords

• nonn
• cons

Comments

See A199170 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least: -1.5093390624666881234512526417921902931351...
greatest: 3.44428460990495541079195552785381251956...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199170.

Programs

Mathematica

a = 1; b = 3; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.6, -1.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199184 least of four roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.44, 3.45}, WorkingPrecision -> 110]
RealDigits[r]  (* A199185 greatest of four roots *)