A199186 Decimal expansion of x<0 satisfying x^2+3*x*cos(x)=3.

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

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

			negative: -1.6364435519550414220675930311871282455...
positive:  3.56968633396230393049792896687800143343...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199170.

Programs

Mathematica

a = 1; b = 3; c = 3;
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}}]
Plot[{f[x], g[x]}, {x, 0, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]
RealDigits[r]  (* A199186 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.56, 3.57}, WorkingPrecision -> 110]
RealDigits[r]  (*  A199187 *)