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

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

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

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

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

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

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

%e least x: 0.369948170589866528691602088620295223...

%e greatest x: 0.7633945382101923369926745363848376145...

%t a = 4; b = -4; 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, .36, .37}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198373 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .76, .77}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198374 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 24 2011