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A198351 Decimal expansion of least x having 4*x^2+x=2*cos(x). 3

%I

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

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

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

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

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

%e least x: -0.74421989852706246873275828006370...

%e greatest x: 0.541418903172906711296921967206240...

%t a = 4; b = 1; c = 2;

%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, -.8, -.7}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198351 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .5, .6}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198352 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 23 2011

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Last modified October 18 10:53 EDT 2021. Contains 348067 sequences. (Running on oeis4.)