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

%I #7 Aug 09 2021 14:13:08

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

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

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

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

%C See A199429 for a guide to related sequences. The Mathematica program includes a graph.

%e x=0.95029497686994665856209249419440178367487...

%t a = 3; b = -2; 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, .95, .96}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199509 *)

%Y Cf. A199429.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 07 2011