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

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

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

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

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

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

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

%e negative: -1.126299940993877523992867733641868507222...

%e positive: 0.559372170813127047765629647326548920708...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -1.13, -1.12}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199154 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .55, .56}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199155 *)

%Y Cf. A198866.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 03 2011