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A198353 Decimal expansion of least x having 4*x^2+x=3*cos(x). 3

%I

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

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

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

%N Decimal expansion of least 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 September 26 06:16 EDT 2021. Contains 347664 sequences. (Running on oeis4.)