A198116 - OEIS

%I #5 Mar 30 2012 18:57:53

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

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

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

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

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

%e least x: -1.1066958928635031236059456759208208...

%e greatest x: 0.80159198729974720435776444320005779...

%t a = 2; b = 1; c = 3;

%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] (* A198116 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .8, .9}, WorkingPrecision -> 110]

%t RealDigits[r2](* A198117 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,4

%A _Clark Kimberling_, Oct 21 2011