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A200300 Decimal expansion of greatest x satisfying 4*x^2 - 3*cos(x) = sin(x). 3

%I

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

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

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

%N Decimal expansion of greatest x satisfying 4*x^2 - 3*cos(x) = sin(x).

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

%H G. C. Greubel, <a href="/A200300/b200300.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.661826141188850993743026123357094...

%e greatest x: 0.8308503276605474027666209935665...

%t a = 4; b = -3; c = 1;

%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, -.67, -.66}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200299 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .83, .84}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200300 *)

%o (PARI) a=4; b=-3; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 15 2011

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Last modified July 31 17:39 EDT 2021. Contains 346376 sequences. (Running on oeis4.)