A200226 - OEIS

%I #8 Jul 01 2018 08:34:40

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

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

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

%N Decimal expansion of greatest x satisfying 3*x^2 - cos(x) = 3*sin(x).

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

%H G. C. Greubel, <a href="/A200226/b200226.txt">Table of n, a(n) for n = 1..10000</a>

%e least x: -0.25837586008348694859843826122973...

%e greatest x: 1.012265562969209417334554419938...

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

%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.26, -.25}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A200225 *)

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

%t RealDigits[r]    (* A200226 *)

%o (PARI) a=3; b=-1; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 30 2018

%Y Cf. A199949.

%K nonn,cons

%O 1,4

%A _Clark Kimberling_, Nov 14 2011