A198114 - OEIS

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

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

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

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

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

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

%e least x: -1.01705490067506096933116558361774...

%e greatest x: 0.66996816904693319175093928956216628...

%t a = 2; b = 1; 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](* A198114 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .66, .67}, WorkingPrecision -> 110]

%t RealDigits[r2](* A198115 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,4

%A _Clark Kimberling_, Oct 21 2011