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%I A200107 #8 Jun 25 2018 22:54:07
%S A200107 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 A200107 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 A200107 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 A200107 Decimal expansion of least x satisfying 2*x^2 - cos(x) = sin(x), negated.
%C A200107 See A199949 for a guide to related sequences.  The Mathematica program includes a graph.
%H A200107 G. C. Greubel, <a href="/A200107/b200107.txt">Table of n, a(n) for n = 0..10000</a>
%e A200107 least x: -0.4690323711198093057335493058025105005500...
%e A200107 greatest x: 0.84026351771576789934797349964835579736...
%t A200107 a = 2; b = -1; c = 1;
%t A200107 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200107 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200107 r = x /. FindRoot[f[x] == g[x], {x, -.47, -.46}, WorkingPrecision -> 110]
%t A200107 RealDigits[r]  (* A200107 *)
%t A200107 r = x /. FindRoot[f[x] == g[x], {x, .84, .85}, WorkingPrecision -> 110]
%t A200107 RealDigits[r]  (* A200108 *)
%o A200107 (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 A200107 Cf. A199949.
%K A200107 nonn,cons
%O A200107 0,1
%A A200107 _Clark Kimberling_, Nov 13 2011

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