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A200295 Decimal expansion of least x satisfying 4*x^2 - 2*cos(x) = 3*sin(x), negated. 3

%I

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

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

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

%N Decimal expansion of least x satisfying 4*x^2 - 2*cos(x) = 3*sin(x), negated.

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

%H G. C. Greubel, <a href="/A200295/b200295.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.40500714967330681353010125636730...

%e greatest x: 0.949145719423009844818919670857...

%t a = 4; b = -2; c = 3;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -.41, -.40}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200295 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .94, .95}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200296 *)

%o (PARI) a=4; b=-2; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 15 2011

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Last modified October 20 04:37 EDT 2019. Contains 328247 sequences. (Running on oeis4.)