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%I #5 Mar 30 2012 18:57:58
%S 3,0,1,7,9,6,3,0,8,1,0,6,8,6,2,8,8,7,2,6,6,7,8,1,4,4,3,3,8,8,5,7,6,8,
%T 9,7,0,3,7,8,3,2,7,2,9,4,7,3,8,3,3,3,0,9,4,0,6,2,7,6,8,4,4,5,7,5,7,0,
%U 0,2,3,7,8,0,9,9,2,1,2,9,5,1,4,6,0,3,3,7,8,7,6,8,4,3,4,7,5,0,7
%N Decimal expansion of greatest x satisfying x^2+3*x*cos(x)=sin(x).
%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.
%e least: -0.93049500263597010976334102402547851258644...
%e greatest: 3.01796308106862887266781443388576897037832...
%t a = 1; b = 3; c = 1;
%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -1.5, 3.5}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199605, least of 4 roots *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199606, greatest of 4 roots *)
%Y Cf. A199597.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Nov 08 2011
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