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

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

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

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

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

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

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

%e least x: -1.21501298426435245704887128499150254...

%e greatest x: 0.460194997750930971424797277964558861...

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

%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, -1.3, -1.2}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A198371 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .46, .47}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198372 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 24 2011