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

%I #6 Mar 30 2012 18:57:53

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

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

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

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

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

%e least x: -1.85071744156198290129787883145887449239...

%e greatest x: 0.38772212025498533427185200524832923...

%t a = 1; b = 2; 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, -1.9, -1.8}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A197841 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .38, .39}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A197842 *)

%Y Cf. A197737.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 20 2011