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A200225 Decimal expansion of least x satisfying 3*x^2 - cos(x) = 3*sin(x), negated. 3

%I

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

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

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

%N Decimal expansion of least x satisfying 3*x^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="/A200225/b200225.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.25837586008348694859843826122973...

%e greatest x: 1.012265562969209417334554419938...

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

%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, -.26, -.25}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200225 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200226 *)

%o (PARI) a=3; b=-1; c=3; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 30 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 14 2011

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Last modified January 29 04:57 EST 2020. Contains 331335 sequences. (Running on oeis4.)