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A198107 Decimal expansion of greatest x having x^2+3x=3*cos(x). 3

%I #7 Aug 09 2021 07:36:44

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

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

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

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

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

%e least x: -2.19856133546816188233076436710906...

%e greatest x: 0.6525732515333974244412623453464...

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

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

%t Plot[{f[x], g[x]}, {x, -3, 1}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, -2.2, -2.1}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198106 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .64, .65}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198107 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 21 2011

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)