A200299 - OEIS

%I #9 Jul 09 2018 19:48:42

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

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

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

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

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

%H G. C. Greubel, <a href="/A200299/b200299.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.661826141188850993743026123357094...

%e greatest x: 0.8308503276605474027666209935665...

%t a = 4; b = -3; c = 1;

%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, -.67, -.66}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200299 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .83, .84}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200300 *)

%o (PARI) a=4; b=-3; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 15 2011