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A199076 Decimal expansion of x>0 satisfying 2*x^2+3*sin(x)=3.

%I A199076 #8 Feb 07 2025 16:44:05
%S A199076 7,1,7,0,8,6,3,8,9,1,8,1,9,2,1,8,2,6,6,9,7,0,0,4,2,9,5,3,3,3,3,0,7,7,
%T A199076 1,8,7,3,8,6,3,1,8,4,1,8,2,8,5,8,2,3,0,6,4,5,9,4,3,8,2,5,1,8,4,8,5,7,
%U A199076 2,8,6,7,3,5,4,3,7,1,4,5,9,0,1,0,5,6,5,4,4,1,6,8,9,7,6,4,5,5,0
%N A199076 Decimal expansion of x>0 satisfying 2*x^2+3*sin(x)=3.
%C A199076 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199076 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199076 negative: -1.72678532237109319694171416856349946617...
%e A199076 positive:  0.71708638918192182669700429533330771873...
%t A199076 a = 2; b = 3; c = 3;
%t A199076 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199076 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199076 r = x /. FindRoot[f[x] == g[x], {x, -1.8, -1.7}, WorkingPrecision -> 110]
%t A199076 RealDigits[r](* A199075 *)
%t A199076 r = x /. FindRoot[f[x] == g[x], {x, .71, .72}, WorkingPrecision -> 110]
%t A199076 RealDigits[r](* A199076 *)
%Y A199076 Cf. A198866.
%K A199076 nonn,cons
%O A199076 0,1
%A A199076 _Clark Kimberling_, Nov 03 2011