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

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

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

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

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

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

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

%e least x: -1.379323320986887658637256189560173787662...

%e greatest x: 0.2110472944900402842082192926601908288...

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

%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, -1.4, -1.3}, WorkingPrecision -> 110]

%t RealDigits[r1](* A198236 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .21, .22}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A198237 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 23 2011