A199668 - OEIS

%I #8 Feb 08 2025 22:26:54

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

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

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

%N Decimal expansion of x>0 satisfying 3*x^2+2*x*cos(x)=3*sin(x).

%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.

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

%e 0.3539044590707670096900071027246646469912...

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

%t f[x_] := a*x^2 + b*x*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, .35, .36}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199668 *)

%Y Cf. A199597.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Nov 09 2011