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A198125 Decimal expansion of greatest x having 2*x^2+2x=cos(x).

%I A198125 #6 Feb 07 2025 16:44:04
%S A198125 3,4,8,4,9,5,0,4,8,1,7,3,8,4,2,9,1,6,5,5,6,6,8,4,1,8,4,7,1,9,9,0,5,9,
%T A198125 9,3,9,6,1,7,9,0,4,1,3,8,9,4,7,5,1,8,9,5,3,6,0,4,1,6,1,8,2,0,6,2,1,8,
%U A198125 2,5,6,7,0,2,6,2,9,1,6,0,5,9,4,5,9,2,4,8,6,5,3,5,4,0,3,6,1,8,4
%N A198125 Decimal expansion of greatest x having 2*x^2+2x=cos(x).
%C A198125 See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e A198125 least x: -1.1678731527385671979308122427699630...
%e A198125 greatest x: 0.34849504817384291655668418471990...
%t A198125 a = 2; b = 2; c = 1;
%t A198125 f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t A198125 Plot[{f[x], g[x]}, {x, -2, 1}]
%t A198125 r1 = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t A198125 RealDigits[r1](* A198124 *)
%t A198125 r2 = x /. FindRoot[f[x] == g[x], {x, .34, .35}, WorkingPrecision -> 110]
%t A198125 RealDigits[r2](* A198125 *)
%Y A198125 Cf. A197737.
%K A198125 nonn,cons
%O A198125 0,1
%A A198125 _Clark Kimberling_, Oct 22 2011