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A198124 Decimal expansion of least x having 2*x^2+2x=cos(x).

%I A198124 #6 Feb 07 2025 16:44:04
%S A198124 1,1,6,7,8,7,3,1,5,2,7,3,8,5,6,7,1,9,7,9,3,0,8,1,2,2,4,2,7,6,9,9,6,3,
%T A198124 0,8,1,7,5,4,3,1,1,3,5,6,7,0,9,6,3,3,5,0,8,3,6,5,3,9,2,4,5,1,0,0,6,7,
%U A198124 5,4,6,9,5,2,1,7,2,6,9,0,0,0,3,0,3,1,4,3,2,3,5,5,8,4,9,8,1,5,1
%N A198124 Decimal expansion of least x having 2*x^2+2x=cos(x).
%C A198124 See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e A198124 least x: -1.1678731527385671979308122427699630...
%e A198124 greatest x: 0.3484950481738429165566841847199059939...
%t A198124 a = 2; b = 2; c = 1;
%t A198124 f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t A198124 Plot[{f[x], g[x]}, {x, -2, 1}]
%t A198124 r1 = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t A198124 RealDigits[r1](* A198124 *)
%t A198124 r2 = x /. FindRoot[f[x] == g[x], {x, .34, .35}, WorkingPrecision -> 110]
%t A198124 RealDigits[r2](* A198125 *)
%Y A198124 Cf. A197737.
%K A198124 nonn,cons
%O A198124 1,3
%A A198124 _Clark Kimberling_, Oct 22 2011