A200230 - OEIS

%I #11 Feb 12 2025 13:04:30

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

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

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

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

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

%H G. C. Greubel, <a href="/A200230/b200230.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e least x: -0.6010846085447445780840915757937924370...

%e greatest x: 0.83362047030745407827417017871253212...

%t a = 3; b = -2; c = 1;

%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, -.61, -.60}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200229 *)

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

%t RealDigits[r]   (* A200230 *)

%o (PARI) a=3; b=-2; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 30 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 14 2011