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A198358 Decimal expansion of greatest x having 4*x^2+2x=cos(x). 3

%I

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

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

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

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

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

%e least x: -0.7460743621285644617325741898565306735...

%e greatest x: 0.29900587455031735703746835072454193932...

%t a = 4; b = 2; c = 1;

%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, -.8, -.7}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198357 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .29, .30}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198358 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 24 2011

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Last modified January 27 04:57 EST 2020. Contains 331291 sequences. (Running on oeis4.)