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 A198140 Decimal expansion of least x having x^2-2x=-3*cos(x). Decimal expansion of greatest x having x^2-2x=-3*cos(x). 3

%I

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

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

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

%N Decimal expansion of least x having x^2-2x=-3*cos(x). Decimal expansion of greatest x having x^2-2x=-3*cos(x).

%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.

%e least x: 1.25361062916653958630784246694528362...

%e greatest x: 2.99155642389786356257272264824822031...

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

%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]

%t Plot[{f[x], g[x]}, {x, -1, 4}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, 1.25, 1.26}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198140 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198141 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 21 2011

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Last modified May 28 05:47 EDT 2022. Contains 354112 sequences. (Running on oeis4.)