A199510 - OEIS

%I #8 Feb 08 2025 10:01:47

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

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

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

%N Decimal expansion of x>0 satisfying 3*x^2-2*x*sin(x)=3*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 1.05111022884372801142571145811941968512...

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

%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, 1.05, 1.06}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199510 *)

%Y Cf. A199429.

%K nonn,cons,changed

%O 1,3

%A _Clark Kimberling_, Nov 07 2011