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%I #5 Mar 30 2012 18:57:58
%S 3,0,4,8,1,3,8,5,9,5,3,6,5,1,1,6,6,8,9,1,4,4,6,0,5,0,5,9,3,7,3,9,0,5,
%T 2,2,0,8,5,4,6,4,6,8,6,6,9,9,5,5,4,2,6,9,2,1,5,9,2,4,3,6,0,5,4,8,2,5,
%U 1,2,3,3,6,9,6,4,0,1,1,0,6,2,4,0,2,2,9,6,6,8,6,6,4,7,6,6,7,6,8
%N Decimal expansion of greatest x satisfying x^2+3*x*cos(x)=2*sin(x).
%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%e least: -0.5973392503648539750049736135997669028331...
%e greatest: 3.0481385953651166891446050593739052208...
%t a = 1; b = 3; 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, -.6, -.5}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199607, least of 4 roots *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199708, greatest of 4 roots *)
%Y Cf. A199597.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Nov 08 2011