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A198123 Decimal expansion of greatest x having 2*x^2-4x=-cos(x).

%I A198123 #6 Feb 07 2025 16:44:04
%S A198123 2,1,2,3,6,3,3,3,3,4,5,1,9,9,8,2,3,9,4,1,9,8,7,7,0,2,4,6,4,1,1,0,6,1,
%T A198123 4,6,7,9,0,2,8,1,7,3,9,1,0,9,6,7,7,3,4,1,9,2,3,6,9,5,8,2,4,7,6,4,8,6,
%U A198123 0,7,5,3,6,7,3,0,0,4,0,4,0,3,9,0,5,4,2,9,6,4,9,6,8,8,6,0,6,3,6
%N A198123 Decimal expansion of greatest x having 2*x^2-4x=-cos(x).
%C A198123 See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e A198123 least x: 0.27932077973816506128059339665539554...
%e A198123 greatest x: 2.123633334519982394198770246411061...
%t A198123 a = 2; b = -4; c = -1;
%t A198123 f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t A198123 Plot[{f[x], g[x]}, {x, -1, 3}]
%t A198123 r1 = x /. FindRoot[f[x] == g[x], {x, .27, .28}, WorkingPrecision -> 110]
%t A198123 RealDigits[r1](* A198122 *)
%t A198123 r2 = x /. FindRoot[f[x] == g[x], {x, 2.1, 2.2}, WorkingPrecision -> 110]
%t A198123 RealDigits[r2](* A198123 *)
%Y A198123 Cf. A197737.
%K A198123 nonn,cons
%O A198123 1,1
%A A198123 _Clark Kimberling_, Oct 21 2011