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Decimal expansion of least x satisfying x+4*cos(x)=0.
3

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

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

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

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

%N Decimal expansion of least x satisfying x+4*cos(x)=0.

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

%e least: -1.25235323400258876318632812197538043590128...

%e greatest: 3.59530486716154799187760693508341871491...

%t a = 1; b = 4; c = 0;

%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, -1.3, -1.2}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199611, least of 4 roots *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199612, greatest of 4 roots *)

%Y Cf. A199597.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 08 2011