A200131 - OEIS

%I #12 Feb 12 2025 13:01:20

%S 1,3,6,8,1,4,9,1,1,2,0,4,2,0,6,7,6,6,7,9,9,7,6,9,9,1,0,8,8,9,0,6,9,2,

%T 6,6,7,5,9,0,3,6,3,8,6,9,7,9,8,2,3,5,6,8,8,7,6,8,3,8,1,0,1,7,8,4,0,2,

%U 0,0,9,5,7,2,9,5,6,3,9,7,4,8,1,6,1,3,1,7,9,1,3,4,2,8,1,1,0,1,7

%N Decimal expansion of greatest x satisfying 2*x^2 - 4*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="/A200131/b200131.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e least x: -0.719005064558842927859271780848179382...

%e greatest x: 1.368149112042067667997699108890...

%t a = 2; b = -4; c = 3;

%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.72, -.71}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200130 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.36, 1.37}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200131 *)

%o (PARI) a=2; b=-4; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 01 2018

%Y Cf. A199949.

%K nonn,cons,changed

%O 1,2

%A _Clark Kimberling_, Nov 14 2011