|
%I #5 Mar 30 2012 18:57:54
%S 7,2,1,3,4,1,3,0,7,6,4,8,0,1,5,5,8,2,4,2,1,0,3,1,7,2,2,8,7,2,3,0,6,4,
%T 4,8,0,7,1,3,2,7,4,5,7,8,8,7,2,6,1,7,7,3,1,8,9,8,8,0,8,7,2,0,6,2,1,0,
%U 8,1,3,0,5,2,7,1,2,8,1,1,4,2,2,4,1,6,5,1,3,1,8,1,0,5,3,3,5,2,3
%N Decimal expansion of greatest x having 3*x^2+2x=4*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: -1.146069580210441813394351195780611...
%e greatest x: 0.721341307648015582421031722872306448...
%t a = 3; b = 2; 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, -1.2, -1.1}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A198228 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, .72, .73}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A198229 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 23 2011
|
