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A199604 Decimal expansion of greatest x satisfying x+3*cos(x) = 0.

%I A199604 #11 Feb 07 2025 19:49:48
%S A199604 2,9,3,8,1,0,0,3,9,3,9,7,0,8,1,1,8,0,7,6,5,8,1,3,6,4,7,8,4,2,5,9,1,2,
%T A199604 9,5,9,6,7,0,2,1,8,6,1,7,3,2,2,3,1,0,1,7,8,4,6,7,1,7,6,3,8,5,3,5,4,6,
%U A199604 7,8,5,9,2,9,2,8,3,6,7,4,6,4,2,0,8,7,7,5,5,2,1,0,3,9,6,7,7,7,3,9
%N A199604 Decimal expansion of greatest x satisfying x+3*cos(x) = 0.
%C A199604 See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%H A199604 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199604 least: -1.1701209500026260537060430118589710...
%e A199604 greatest:  2.9381003939708118076581364784259...
%t A199604 a = 1; b = 3; c = 0;
%t A199604 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199604 Plot[{f[x], g[x]}, {x, -1.5, 3.5}, {AxesOrigin -> {0, 0}}]
%t A199604 r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t A199604 RealDigits[r]  (* A199603 least of 4 roots *)
%t A199604 r = x /. FindRoot[f[x] == g[x], {x, 2.93, 2.94}, WorkingPrecision -> 110]
%t A199604 RealDigits[r]  (* A199604 greatest of 4 roots *)
%Y A199604 Cf. A199597.
%K A199604 nonn,cons
%O A199604 1,1
%A A199604 _Clark Kimberling_, Nov 08 2011
%E A199604 a(86) onwards corrected by _Georg Fischer_, Aug 03 2021