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A198354 Decimal expansion of greatest x having 4*x^2+x=3*cos(x). 3

%I

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

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

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

%N Decimal expansion of greatest x having 4*x^2+x=3*cos(x).

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

%e least x: -0.84250907415961557669109359901490911...

%e greatest x: 0.655996424452391548073107130869590...

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

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

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

%t r1 = x /. FindRoot[f[x] == g[x], {x, -.9, -.8}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198353 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .65, .66}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198354 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 23 2011

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Last modified October 24 09:38 EDT 2021. Contains 348225 sequences. (Running on oeis4.)