A199464 - OEIS

%I #6 Mar 30 2012 18:57:57

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

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

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

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

%C See A199429 for a guide to related sequences.  The Mathematica program includes a graph.

%e x=1.02065194455071428179208010985825740916...

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

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

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

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

%t RealDigits[r]  (* A199464 greatest root *)

%Y Cf. A199429.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 07 2011