|
%I #6 Mar 30 2012 18:57:53
%S 4,2,3,4,1,8,8,6,7,4,3,6,9,5,6,3,9,0,2,5,4,9,0,1,9,1,4,5,6,7,1,3,7,9,
%T 8,7,7,8,8,8,1,6,9,1,7,2,9,9,4,8,0,6,3,4,0,9,5,8,5,0,6,3,0,6,0,5,6,7,
%U 1,3,8,3,3,0,6,0,1,9,8,2,1,5,8,2,0,6,1,7,4,1,3,1,2,5,8,5,7,1,2
%N Decimal expansion of least x having 2*x^2-3x=-cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: 0.42341886743695639025490191456713...
%e greatest x: 1.46336282729643114510529642616...
%t a = 2; b = -3; c = -1;
%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, -1, 2}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, -.43, -.42}, WorkingPrecision -> 110]
%t RealDigits[r1](* A198120 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t RealDigits[r2](* A198121 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 21 2011
|
