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 A198230 Decimal expansion of least x having 3*x^2+3x=cos(x). 3

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

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

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

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

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

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

%e least x: -1.126996596111399658345237384325404854...

%e greatest x: 0.2565849342235694401504579474990935...

%t a = 3; b = 3; c = 1;

%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, -1.2, -1.1}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198230 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .25, .26}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198231 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Oct 23 2011

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Last modified May 17 23:39 EDT 2024. Contains 372608 sequences. (Running on oeis4.)