A199469 - OEIS

%I #10 Feb 08 2025 09:59:42

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

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

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

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

%C See A199429 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 2.10283686091410470147276851182470222999...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, 2.1, 2.2}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199469 *)

%Y Cf. A199429.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Nov 07 2011