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A198231 Decimal expansion of greatest x having 3*x^2+3x=cos(x). 3

%I #6 Mar 30 2012 18:57:54

%S 2,5,6,5,8,4,9,3,4,2,2,3,5,6,9,4,4,0,1,5,0,4,5,7,9,4,7,4,9,9,0,9,3,5,

%T 5,9,7,4,9,3,1,3,4,1,1,9,4,6,0,6,7,2,9,3,7,2,5,2,0,1,7,4,8,4,7,5,7,2,

%U 0,4,3,3,0,3,2,9,1,8,9,9,0,1,8,4,9,6,1,4,3,3,4,1,3,0,9,1,2,6,9

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

%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.

%e least x: -1.1269965961113996583452373843254048549...

%e greatest x: 0.25658493422356944015045794749909355...

%t a = 3; b = 3; 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] (* A198230 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .25, .26}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198231 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 23 2011

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