A198138 - OEIS

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

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

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

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

%N Decimal expansion of least x having 3*x^2+4x=4*cos(x).

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

%e least x: -1.447057151041655078779471681449880627...

%e greatest x: 0.5817200797316597228428659232714882...

%t a = 3; b = 4; 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, -1.5, -1.4}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198138 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .58, .59}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198139 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 23 2011