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

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

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

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

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

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

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

%e x=1.0291249219669069861713592377891164084811711841...

%t a = 2; b = 1; 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, 1.02, 1.03}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199381 *)

%Y Cf. A199370.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 05 2011