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%I #9 Jul 08 2018 21:28:09
%S 7,1,9,3,8,4,2,6,0,4,5,9,8,7,5,8,3,2,1,0,7,5,5,2,4,1,1,5,9,1,3,8,0,6,
%T 1,7,5,5,7,6,3,3,7,2,7,5,5,4,2,4,6,3,4,1,9,6,7,5,8,9,1,7,2,4,8,5,5,8,
%U 5,3,7,4,4,4,3,4,0,5,7,4,5,9,8,7,5,5,2,9,0,4,2,5,1,9,8,0,5,8,3
%N Decimal expansion of greatest x satisfying 4*x^2 - cos(x) = 2*sin(x).
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200288/b200288.txt">Table of n, a(n) for n = 0..10000</a>
%e least x: -0.300931885421902370031006240717514956...
%e greatest x: 0.7193842604598758321075524115913806...
%t a = 4; 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, -1, 1}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.31, -.30}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200287 *)
%t r = x /. FindRoot[f[x] == g[x], {x, .71, .72}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200288 *)
%o (PARI) a=4; b=-1; c=2; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 07 2018
%Y Cf. A199949.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Nov 15 2011
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