A199451 - OEIS

%I #8 Feb 08 2025 09:35:29

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

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

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

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

%C See A199370 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 0.69083618120542648136837155873197312749631762...

%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, .69, .70}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199451 *)

%Y Cf. A199429.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 06 2011