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

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

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

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

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

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

%C See A199370 for a guide to related sequences. The Mathematica program includes a graph.

%e x=0.756321432095254744378797425250754254953980...

%t a = 2; 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, .75, .76}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199442 *)

%Y Cf. A199429.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 06 2011