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

%I #5 Mar 30 2012 18:57:58

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

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

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

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

%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.

%e x=0.5910476680725495873978098454642124730516901364280...

%t a = 3; b = -1; c = 1;

%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .59, .60}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199797 *)

%Y Cf. A199597.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 10 2011