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A200018 Decimal expansion of least x satisfying x^2 - 2*cos(x) = sin(x) (negated). 3

%I #11 Jun 25 2018 03:50:20

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

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

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

%N Decimal expansion of least x satisfying x^2 - 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="/A200018/b200018.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.8096299991295524131861096984840271321...

%e greatest x: 1.254187962477919553363912326321801374...

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

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

%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.9, -.8}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200018 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200019 *)

%o (PARI) a=1; b=-2; 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 12 2011

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