A200242 - OEIS

%I #13 Jun 25 2018 03:50:41

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

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

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

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

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

%H G. C. Greubel, <a href="/A200242/b200242.txt">Table of n, a(n) for n = 1..10000</a>

%e least x: -0.495594232798110803966694081360666...

%e greatest x: 1.2559670249437296288542832153976444...

%t a = 3; b = -3; 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, -.50, -.49}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200241 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.25, 1.26}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200242 *)

%o (PARI) a=3; b=-3; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018

%Y Cf. A199949.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 15 2011