%I #9 Jul 09 2018 19:49:24
%S 1,0,1,6,1,4,3,9,5,6,7,2,3,5,5,8,7,3,3,7,9,9,4,5,5,9,0,1,2,9,6,8,6,4,
%T 7,4,6,8,7,7,9,9,4,9,2,5,9,9,2,1,9,8,1,9,8,1,9,0,3,6,6,3,3,4,1,4,8,1,
%U 0,7,6,3,7,0,8,3,4,4,0,9,5,0,4,4,0,1,3,4,3,9,8,5,6,2,0,2,9,6,9
%N Decimal expansion of greatest x satisfying 4*x^2 - 3*cos(x) = 3*sin(x).
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200302/b200302.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: -0.52377415675325572171784049673944...
%e greatest x: 1.016143956723558733799455901296...
%t a = 4; b = -3; c = 3;
%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.54, -.51}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200297 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1, 1.05}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200298 *)
%o (PARI) a=4; b=-3; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018
%Y Cf. A199949.
%K nonn,cons
%O 1,4
%A _Clark Kimberling_, Nov 15 2011
|