A200279 - OEIS

%I #9 Jul 08 2018 21:26:55

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

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

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

%N Decimal expansion of least x satisfying 3*x^2 - 4*cos(x) = 2*sin(x), negated.

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

%H G. C. Greubel, <a href="/A200279/b200279.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.73563807644468208614776955612311...

%e greatest x: 1.096406992421267947221987681314...

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

%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, -.74, -.73}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200279 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200280 *)

%o (PARI) a=3; b=-4; c=2; 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