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Decimal expansion of x>0 satisfying 2*x^2+2*x*sin(x)=3.
1

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

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

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

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

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

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

%e x=0.89521974443582001297087274636196596748905653...

%t a = 2; b = 2; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -1, Pi}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .89, .90}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199383 *)

%Y Cf. A199370.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 05 2011