A199513 - OEIS

%I #5 Mar 30 2012 18:57:57

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

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

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

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

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

%e x=1.14967454409407837060286558757515943034710...

%t a = 3; 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, 1.14, 1.15}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199513 *)

%Y Cf. A199429.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 07 2011