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Decimal expansion of least x having 4*x^2+3x=cos(x).
4

%I #5 Mar 30 2012 18:57:54

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

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

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

%N Decimal expansion of least x having 4*x^2+3x=cos(x).

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

%e least x: -0.91615106109683577000135072803946391...

%e greatest x: 0.244045322629135591466858282939448079493...

%t a = 4; b = 3; 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, -1, -.9}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198361 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .24, .25}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198362 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 24 2011