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

%I #5 Mar 30 2012 18:57:54

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

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

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

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

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

%e least x: -1.128864420523986139477004663061889573...

%e greatest x: 0.6060777836486264536657977579905629...

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

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

%t Plot[{f[x], g[x]}, {x, -2, 1}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198367 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .60, .61}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198368 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Oct 24 2011