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%I #5 Mar 30 2012 18:57:53
%S 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 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 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 Decimal expansion of greatest x having 2*x^2+2x=cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: -1.1678731527385671979308122427699630...
%e greatest x: 0.34849504817384291655668418471990...
%t a = 2; b = 2; c = 1;
%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, -2, 1}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t RealDigits[r1](* A198124 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, .34, .35}, WorkingPrecision -> 110]
%t RealDigits[r2](* A198125 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 22 2011