%I #12 Jul 09 2018 19:46:05
%S 1,2,8,6,1,2,8,0,2,6,7,4,5,9,0,9,9,6,5,2,7,9,1,5,1,1,2,6,1,4,6,3,7,9,
%T 4,2,3,5,1,2,6,4,2,7,5,6,5,2,8,4,4,1,9,4,6,0,0,6,6,9,7,2,2,3,6,1,3,0,
%U 5,8,2,2,0,3,8,5,4,0,6,3,0,8,7,8,1,6,4,5,6,4,8,4,3,6,3,8,2,8,2
%N Decimal expansion of greatest x satisfying 3*x^2 - 4*cos(x) = 4*sin(x), negated.
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200284/b200284.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: -0.5959294541202234263223480673526214...
%e greatest x: 1.28612802674590996527915112614637...
%t a = 3; b = -4; c = 4;
%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, -.6, -.59}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200283 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200284 *)
%o (PARI) a=3; b=-4; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 07 2018
%Y Cf. A199949.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 15 2011
|