A198224 - OEIS

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

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

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

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

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

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

%e least x: -1.014060582687901072214777706552979973...

%e greatest x: 0.500866310253011769790802754694656330...

%t a = 3; b = 2; 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, -1.02, -1.01}, WorkingPrecision -> 110]

%t RealDigits[r1]  (* A198224 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .5, .51}, WorkingPrecision -> 110]

%t RealDigits[r2]  (* A198225 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,4

%A _Clark Kimberling_, Oct 22 2011