A200288 - OEIS

%I #10 Feb 07 2025 16:44:06

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

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

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

%N Decimal expansion of greatest x satisfying 4*x^2 - cos(x) = 2*sin(x).

%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.

%H G. C. Greubel, <a href="/A200288/b200288.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.300931885421902370031006240717514956...

%e greatest x: 0.7193842604598758321075524115913806...

%t a = 4; b = -1; c = 2;

%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, -.31, -.30}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A200287 *)

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

%t RealDigits[r]   (* A200288 *)

%o (PARI) a=4; b=-1; c=2; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 07 2018

%Y Cf. A199949.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Nov 15 2011