A198119 - OEIS

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

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

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

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

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

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

%e least x: -1.1690226923053929102101002288527830...

%e greatest x: 0.89565238135842890121817647213537147...

%t a = 2; b = 1; 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, -1.17, -1.16}, WorkingPrecision -> 110]

%t RealDigits[r1](* A198118 *)

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

%t RealDigits[r2](* A198119 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 21 2011