%I #9 Jul 06 2018 03:03:29
%S 9,3,0,0,5,7,1,1,0,0,9,2,4,8,9,2,4,6,7,8,8,2,4,6,8,1,4,4,0,5,6,4,2,9,
%T 8,7,6,1,2,8,2,5,6,1,0,1,9,3,3,3,0,7,7,4,3,6,2,1,4,0,0,8,2,0,5,2,4,8,
%U 3,3,0,7,8,7,5,2,4,1,7,9,3,2,7,7,1,6,9,0,3,3,2,7,7,5,3,4,1,1,2
%N Decimal expansion of greatest x satisfying 3*x^2 - 3*cos(x) = sin(x).
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200238/b200238.txt">Table of n, a(n) for n = 0..10000</a>
%e least x: -0.725773931375098148951813264652313...
%e greatest x: 0.9300571100924892467882468144056...
%t a = 3; b = -3; c = 1;
%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.73, -.72}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200237 *)
%t r = x /. FindRoot[f[x] == g[x], {x, .93, .94}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200238 *)
%o (PARI) a=3; b=-3; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018
%Y Cf. A199949.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Nov 15 2011