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

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

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

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

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

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

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

%e x=0.809476415875062266835317913845989194004148255...

%t a = 3; b = -1; 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, .80, .81}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199506 *)

%Y Cf. A199429.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 07 2011