A200283 - OEIS

%I #9 Jul 08 2018 21:27:32

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

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

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

%N Decimal expansion of least 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="/A200283/b200283.txt">Table of n, a(n) for n = 0..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 0,1

%A _Clark Kimberling_, Nov 15 2011