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A198129 Decimal expansion of greatest x having 2*x^2+3x=cos(x).

%I A198129 #6 Feb 07 2025 16:44:04
%S A198129 1,5,1,7,5,3,8,9,8,0,6,6,1,4,8,2,2,4,4,8,3,2,7,4,6,9,8,6,3,9,0,8,1,1,
%T A198129 5,0,8,0,9,9,5,0,7,1,0,7,8,4,5,4,2,2,8,5,8,6,9,0,1,4,6,0,6,0,6,1,6,8,
%U A198129 2,6,6,7,2,5,9,4,1,1,6,4,7,4,3,7,3,9,2,5,7,7,1,3,3,9,9,5,0,6,7
%N A198129 Decimal expansion of greatest x having 2*x^2+3x=cos(x).
%C A198129 See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e A198129 least x: -1.51753898066148224483274698639081150...
%e A198129 greatest x: 0.271831851895805907186882033358839...
%t A198129 a = 2; b = 3; c = 1;
%t A198129 f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t A198129 Plot[{f[x], g[x]}, {x, -2, 1}]
%t A198129 r1 = x /. FindRoot[f[x] == g[x], {x, -1.52, -1.51}, WorkingPrecision -> 110]
%t A198129 RealDigits[r1](* A198128 *)
%t A198129 r2 = x /. FindRoot[f[x] == g[x], {x, .27, .28}, WorkingPrecision -> 110]
%t A198129 RealDigits[r2](* A198129 *)
%Y A198129 Cf. A197737.
%K A198129 nonn,cons
%O A198129 0,2
%A A198129 _Clark Kimberling_, Oct 22 2011