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A200026 Decimal expansion of least x satisfying x^2 - 3*cos(x) = sin(x) (negated). 3

%I

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

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

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

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

%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.

%H G. C. Greubel, <a href="/A200026/b200026.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.9559087984816134135373014395844...

%e greatest x: 1.31448560919776196551921986761091...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -.96, -.95}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200026 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.31, 1.34}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200027 *)

%o (PARI) a=1; b=-3; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 13 2011

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Last modified October 18 08:08 EDT 2019. Contains 328146 sequences. (Running on oeis4.)