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A199157 Decimal expansion of x>0 satisfying 3*x^2+2*sin(x)=3.

%I A199157 #8 Feb 07 2025 16:44:05
%S A199157 7,4,1,4,5,6,7,0,6,7,6,9,8,5,8,9,2,0,1,5,9,4,6,0,9,5,6,3,4,9,1,0,8,9,
%T A199157 4,9,9,8,7,5,4,6,6,1,4,9,6,5,7,8,0,9,0,1,8,9,5,5,5,0,1,0,3,5,1,0,4,9,
%U A199157 6,6,0,9,9,0,4,8,0,8,3,1,6,2,7,9,1,9,8,9,1,1,9,4,5,2,6,4,8,4,3
%N A199157 Decimal expansion of x>0 satisfying 3*x^2+2*sin(x)=3.
%C A199157 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199157 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199157 negative: -1.280117027823592900045689845558554979655...
%e A199157 positive:  0.741456706769858920159460956349108949987...
%t A199157 a = 3; b = 2; c = 3;
%t A199157 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199157 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199157 r = x /. FindRoot[f[x] == g[x], {x, -1.29, -1.28}, WorkingPrecision -> 110]
%t A199157 RealDigits[r]   (* A199156 *)
%t A199157 r = x /. FindRoot[f[x] == g[x], {x, .74, .75}, WorkingPrecision -> 110]
%t A199157 RealDigits[r]  (* A199157 *)
%Y A199157 Cf. A198866.
%K A199157 nonn,cons
%O A199157 0,1
%A A199157 _Clark Kimberling_, Nov 03 2011