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%I #11 Jul 06 2018 03:03:13
%S 1,2,1,7,2,4,5,4,2,8,9,4,5,4,5,9,0,2,7,6,9,3,2,4,5,8,6,3,5,4,5,6,0,7,
%T 5,9,8,0,1,4,4,3,6,1,3,7,3,3,1,6,6,6,9,9,0,4,7,4,1,7,5,2,2,5,7,9,2,2,
%U 5,5,9,2,8,8,9,6,7,8,5,5,1,4,3,9,4,3,5,4,6,8,8,7,5,3,5,3,3,4,4
%N Decimal expansion of greatest x satisfying 3*x^2 - 2*cos(x) = 4*sin(x).
%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A200236/b200236.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: -0.37112234946927280533419999688093...
%e greatest x: 1.217245428945459027693245863545...
%t a = 3; b = -2; c = 4;
%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.38, -.37}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200235 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t RealDigits[r] (* A200236 *)
%o (PARI) a=3; b=-2; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018
%Y Cf. A199949.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 14 2011
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