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%I A199775 #9 May 13 2013 01:49:59
%S A199775 1,3,3,1,4,8,6,9,5,9,3,3,5,0,4,0,5,0,3,3,2,7,3,6,3,0,6,9,9,1,7,3,3,9,
%T A199775 5,4,3,0,2,5,8,7,5,9,3,3,5,7,9,9,5,1,5,0,9,6,9,6,3,2,6,4,2,5,4,4,8,5,
%U A199775 8,5,9,0,2,5,5,4,7,7,3,3,3,0,2,3,5,2,2,9,3,3,0,2,9,4,9,4,4,8,3
%N A199775 Decimal expansion of x>0 satisfying 2*x^2 - 2*x*cos(x) = 3*sin(x).
%C A199775 See A199597 for a guide to related sequences.  The Mathematica program includes a graph.
%e A199775 1.331486959335040503327363069917339543025...
%t A199775 a = 2; b = -2; c = 3;
%t A199775 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199775 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A199775 r = x /. FindRoot[f[x] == g[x], {x, 1.33, 1.34}, WorkingPrecision -> 110]
%t A199775 RealDigits[r]   (* A199775 *)
%o A199775 (PARI) solve(x=1,2,2*x^2-2*x*cos(x)-3*sin(x)) \\ _Charles R Greathouse IV_, Dec 28 2011
%Y A199775 Cf. A199597.
%K A199775 nonn,cons
%O A199775 1,2
%A A199775 _Clark Kimberling_, Nov 10 2011

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