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%I A199620 #5 Mar 30 2012 18:57:58
%S A199620 3,4,5,2,8,9,9,8,8,8,5,3,2,9,2,7,7,8,0,3,3,6,3,0,0,8,3,7,8,6,4,9,8,3,
%T A199620 8,8,4,0,8,8,3,6,8,5,5,6,5,7,8,5,1,5,3,8,6,4,0,5,6,2,7,2,9,0,9,5,5,1,
%U A199620 8,5,6,4,0,8,5,9,2,4,4,5,4,6,8,3,0,5,7,0,2,5,8,4,9,8,6,0,9,6,0
%N A199620 Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=4*sin(x).
%C A199620 See A199597 for a guide to related sequences.  The Mathematica program includes a graph.
%e A199620 least: 0.80005334262741575936859027990893321963...
%e A199620 greatest:  3.4528998885329277803363008378649838...
%t A199620 a = 1; b = 4; c = 4;
%t A199620 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199620 Plot[{f[x], g[x]}, {x, -.5, 4}, {AxesOrigin -> {0, 0}}]
%t A199620 r = x /. FindRoot[f[x] == g[x], {x, .8, .81}, WorkingPrecision -> 110]
%t A199620 RealDigits[r]  (* A199619, least pos root *)
%t A199620 r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
%t A199620 RealDigits[r]  (* A199620, greatest of 3 roots *)
%Y A199620 Cf. A199597.
%K A199620 nonn,cons
%O A199620 1,1
%A A199620 _Clark Kimberling_, Nov 08 2011

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