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

%I #8 Aug 09 2021 07:43:31

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

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

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

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

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

%e least x: -0.596628694828122209772071553484966...

%e greatest x: 0.3733959160193969688968321519818...

%t a = 4; b = 1; 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, -.6, -.5}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198349 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .37, .38}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198350 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 23 2011