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A199074 Decimal expansion of x>0 satisfying 2*x^2+3*sin(x)=2.

%I A199074 #8 Feb 07 2025 16:44:05
%S A199074 5,1,3,2,7,4,7,7,7,7,0,2,5,6,8,2,3,4,5,1,7,1,8,5,0,4,2,0,2,4,9,9,0,2,
%T A199074 8,7,6,3,0,7,4,1,4,1,1,3,7,0,7,7,7,1,8,1,7,2,5,5,6,9,9,4,9,2,2,6,8,7,
%U A199074 0,1,5,7,8,5,9,8,2,1,2,8,2,1,4,2,9,2,4,7,4,0,8,2,0,3,1,6,7,5,8
%N A199074 Decimal expansion of x>0 satisfying 2*x^2+3*sin(x)=2.
%C A199074 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199074 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199074 negative: -1.5811135842680126236235133011318966...
%e A199074 positive:  0.5132747777025682345171850420249902...
%t A199074 a = 2; b = 3; c = 2;
%t A199074 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199074 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199074 r = x /. FindRoot[f[x] == g[x], {x, -1.6, -1.5}, WorkingPrecision -> 110]
%t A199074 RealDigits[r](* A199073 *)
%t A199074 r = x /. FindRoot[f[x] == g[x], {x, .51, .52}, WorkingPrecision -> 110]
%t A199074 RealDigits[r](* A199074 *)
%Y A199074 Cf. A198866.
%K A199074 nonn,cons
%O A199074 0,1
%A A199074 _Clark Kimberling_, Nov 03 2011