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A200107 Decimal expansion of least x satisfying 2*x^2 - cos(x) = sin(x), negated. 3

%I #8 Jun 25 2018 22:54:07

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

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

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

%N Decimal expansion of least x satisfying 2*x^2 - 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="/A200107/b200107.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.4690323711198093057335493058025105005500...

%e greatest x: 0.84026351771576789934797349964835579736...

%t a = 2; b = -1; c = 1;

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

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.47, -.46}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200107 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .84, .85}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200108 *)

%o (PARI) a=2; b=-1; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 25 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 13 2011

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)