A198233 - OEIS

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

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

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

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

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

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

%e least x: -1.200777278517391290663654587682671...

%e greatest x: 0.4258157107483169845689223216341480870...

%t a = 3; b = 3; c = 2;

%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, -1.3, -1.2}, WorkingPrecision -> 110]

%t RealDigits[r1](* A198232 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .42, .43}, WorkingPrecision -> 110]

%t RealDigits[r2](* A198233 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 23 2011