A198125 - OEIS

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

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

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

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

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

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

%e least x: -1.1678731527385671979308122427699630...

%e greatest x: 0.34849504817384291655668418471990...

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

%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](* A198124 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .34, .35}, WorkingPrecision -> 110]

%t RealDigits[r2](* A198125 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 22 2011