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%I A199780 #5 Mar 30 2012 18:57:58
%S A199780 1,0,9,4,1,8,7,4,5,1,4,7,9,3,4,4,8,8,1,8,5,5,5,6,0,8,9,0,9,0,2,4,8,5,
%T A199780 1,6,6,2,7,3,2,0,4,4,6,6,3,0,2,8,6,6,4,8,4,1,4,5,0,6,8,6,7,5,0,1,0,6,
%U A199780 7,9,0,0,1,6,6,7,3,2,8,8,2,2,8,6,4,7,5,0,6,2,5,4,7,3,3,9,0,4,4
%N A199780 Decimal expansion of x>0 satisfying 2*x^2-3*x*cos(x)=sin(x).
%C A199780 See A199597 for a guide to related sequences.  The Mathematica program includes a graph.
%e A199780 x=1.094187451479344881855560890902485166...
%t A199780 a = 2; b = -3; c = 1;
%t A199780 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
%t A199780 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A199780 r = x /. FindRoot[f[x] == g[x], {x, 1.09, 1.10}, WorkingPrecision -> 110]
%t A199780 RealDigits[r]   (* A199780 *)
%Y A199780 Cf. A199597.
%K A199780 nonn,cons
%O A199780 1,3
%A A199780 _Clark Kimberling_, Nov 10 2011

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