A200307 - OEIS

%I #9 Jul 10 2018 02:57:35

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

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

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

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

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

%H G. C. Greubel, <a href="/A200307/b200307.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.6174065144201321316882984350723098...

%e greatest x: 1.06740848569359172383926056700706...

%t a = 4; 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, -2, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.62, -.63}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200307 *)

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

%t RealDigits[r]   (* A200308 *)

%o (PARI) a=4; b=-4; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 10 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 16 2011