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

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

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

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

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

%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: -1.1023847462794395958058183658678813...

%e greatest x: 0.203451325531925041555116805060611...

%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, -2, 1}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198369 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .20, .21}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198370 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,4

%A _Clark Kimberling_, Oct 24 2011