|
%I #6 Mar 30 2012 18:57:53
%S 6,7,2,2,5,5,1,6,7,7,3,8,2,5,6,8,8,0,7,4,8,6,0,4,6,1,7,8,7,0,3,2,5,9,
%T 7,6,6,5,7,5,0,9,3,6,8,2,1,3,9,8,1,8,9,5,5,0,1,7,7,5,2,3,5,7,8,1,1,2,
%U 9,5,4,4,7,2,1,2,4,8,1,8,8,7,8,6,0,8,5,0,8,3,4,5,5,2,9,9,8,0,4
%N Decimal expansion of least x having x^2-3x=-2*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: 0.672255167738256880748604617870325976...
%e greatest x: 3.525867901227958617954825081711394...
%t a = 1; b = -3; c = -2;
%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, 0, 4}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, .65, .68}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A198098 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A198099 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 21 2011
|
