A200232 - OEIS

%I #11 Feb 12 2025 13:04:32

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

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

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

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

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

%H G. C. Greubel, <a href="/A200232/b200232.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: -0.508066683701868134653059484203509821...

%e greatest x: 0.9632913766196791046556418296641642...

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

%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, -.51, -.50}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200231 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .96, .97}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200232 *)

%o (PARI) a=3; b=-2; c=2; solve(x=.96, .97, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018

%Y Cf. A199949.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Nov 14 2011