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A198121 Decimal expansion of greatest x having 2*x^2-3x=-cos(x).

%I A198121 #7 Feb 07 2025 16:44:04
%S A198121 1,4,6,3,3,6,2,8,2,7,2,9,6,4,3,1,1,4,5,1,0,5,2,9,6,4,2,6,1,6,1,3,5,8,
%T A198121 7,0,6,9,1,8,2,7,7,3,2,5,2,2,4,4,1,4,1,2,6,9,7,2,5,8,6,5,5,2,8,2,5,0,
%U A198121 0,0,9,8,5,6,6,1,6,1,2,6,5,6,7,7,4,7,4,2,9,8,4,9,2,8,9,7,3,8,4
%N A198121 Decimal expansion of greatest x having 2*x^2-3x=-cos(x).
%C A198121 See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e A198121 least x: 0.423418867436956390254901914567137...
%e A198121 greatest x: 1.4633628272964311451052964261613...
%t A198121 a = 2; b = -3; c = -1;
%t A198121 f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t A198121 Plot[{f[x], g[x]}, {x, -1, 2}]
%t A198121 r1 = x /. FindRoot[f[x] == g[x], {x, -.43, -.42}, WorkingPrecision -> 110]
%t A198121 RealDigits[r1](* A198120 *)
%t A198121 r2 = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A198121 RealDigits[r2](* A198121 *)
%Y A198121 Cf. A197737.
%K A198121 nonn,cons
%O A198121 1,2
%A A198121 _Clark Kimberling_, Oct 21 2011