%I #5 Mar 30 2012 18:57:54
%S 4,1,0,7,3,0,5,6,8,1,0,5,3,1,9,6,7,8,8,4,2,6,1,6,3,2,1,6,8,8,4,2,9,3,
%T 2,6,3,7,9,5,7,1,5,3,6,1,1,2,5,4,5,5,4,5,6,9,4,6,9,7,5,4,1,5,7,2,2,8,
%U 2,7,3,8,9,2,4,0,5,3,7,7,8,6,8,6,6,3,0,0,5,0,5,8,3,1,8,5,8,0,6
%N Decimal expansion of greatest x having 3*x^2+x=cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: -0.6986567055323602628379046584016603229...
%e greatest x: 0.41073056810531967884261632168842932...
%t a = 3; b = 1; c = 1;
%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, -1, 1}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, -.7, -0.6}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A198214 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, 4.1, 4.2}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A198215 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 22 2011
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