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%I #5 Mar 30 2012 18:57:58
%S 3,5,1,5,6,1,3,1,9,9,6,8,7,3,5,8,0,2,3,8,4,2,1,8,0,2,1,0,7,0,4,0,3,0,
%T 7,9,2,2,1,7,8,8,8,8,6,7,9,8,1,9,3,3,5,0,7,3,8,3,3,3,5,6,9,7,8,4,4,2,
%U 4,3,4,5,9,1,6,5,7,2,6,4,8,5,7,2,3,9,2,0,0,0,7,5,7,6,0,2,3,4,1
%N Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=2*sin(x).
%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%e least: -0.856374049744346109322078062564729199476600...
%e greatest: 3.515613199687358023842180210704030792217...
%t a = 1; b = 4; c = 2;
%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.86, -.85}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199615, least of 4 roots *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199616, greatest of 4 roots *)
%Y Cf. A199597.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Nov 08 2011