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

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

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

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

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

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

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

%e least: -3.746168565528221340687013560527596978856...

%e greatest: 1.625278383378448643933003226246836106...

%t a = 1; b = -4; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -4, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -3.8, -3.7}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199733 least root *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199734 greatest root *)

%Y Cf. A199597.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 09 2011