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A200223 Decimal expansion of least x satisfying 3*x^2 - cos(x) = 2*sin(x), negated. 3

%I

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

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

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

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

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

%H G. C. Greubel, <a href="/A200223/b200223.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.3231143338862262845356370492311714...

%e greatest x: 0.84890518832952236173456381626613...

%t a = 3; b = -1; c = 2;

%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, -.33, -.32}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200223 *)

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

%t RealDigits[r] (* A200224 *)

%o (PARI) a=3; b=-1; c=2; 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 February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)