A198235 - OEIS

%I #6 Mar 30 2012 18:57:54

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

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

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

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

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

%e least x: -1.28838923732282692044695376198415263654...

%e greatest x: 0.646435567527722588379133828108743889...

%t a = 3; b = 3; c = 4;

%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](* A198234 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .64, .65}, WorkingPrecision -> 110]

%t RealDigits[r2](* A198235 *)

%Y Cf. A197737

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 23 2011