A198234 - OEIS

%I #7 Mar 30 2012 18:57:54

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

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

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

%N Decimal expansion of least 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 1,2

%A _Clark Kimberling_, Oct 23 2011