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A199182 Decimal expansion of least x satisfying x^2+3*x*cos(x)=1. 4

%I

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

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

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

%N Decimal expansion of least x satisfying x^2+3*x*cos(x)=1.

%C See A199170 for a guide to related sequences. The Mathematica program includes a graph.

%e least: -1.3606727725137972152286027487379925...

%e greatest: 3.27746466341373058734587727791083...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199182 least of four roots *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.27, 3.28}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199183 greatest of four roots *)

%Y Cf. A199170.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 04 2011

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Last modified February 28 10:49 EST 2020. Contains 332323 sequences. (Running on oeis4.)