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

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

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

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

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

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

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

%e least x: -1.0119640719541596551643922516868104...

%e greatest x: 0.4003039952551859146306371868342035...

%t a = 4; b = 3; c = 2;

%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, -1.1, -1.0}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198363 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .4, .41}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198364 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,5

%A _Clark Kimberling_, Oct 24 2011