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Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=4*sin(x).
3

%I #5 Mar 30 2012 18:57:58

%S 1,7,1,7,7,6,1,7,0,1,5,5,9,1,4,6,7,3,7,9,4,6,5,4,6,9,3,7,6,8,3,0,8,4,

%T 0,1,0,8,3,6,6,9,6,2,7,3,2,6,4,6,5,7,0,5,3,1,8,2,8,1,3,5,5,1,1,2,3,7,

%U 5,0,4,2,0,1,0,9,6,6,9,3,3,1,2,8,9,7,5,5,1,6,9,0,7,5,6,1,0,1,3

%N Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=4*sin(x).

%C See A199597 for a guide to related sequences. The Mathematica program includes a graph.

%e least: -3.80284270062359171640437975188554983520...

%e greatest: 1.71776170155914673794654693768308401...

%t a = 1; b = -4; c = 4;

%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -3.9, -3.8}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199731 least of 4 roots *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.71, 1.72}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199732 greatest of 4 roots *)

%Y Cf. A199597.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 09 2011