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

%I #5 Mar 30 2012 18:57:56

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

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

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

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

%C See A198866 for a guide to related sequences. The Mathematica program includes a graph.

%e negative: -2.159478296974116018268923878524689009...

%e positive: 1.1024409927824745029005123269585791156...

%t a = 1; b = 2; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -2.2, -2.1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199050 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]

%t RealDigits[r](* A199051 *)

%Y Cf. A198866.

%K nonn,cons

%O 1,4

%A _Clark Kimberling_, Nov 02 2011