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A196766 Decimal expansion of the slope (negative) at the point of tangency of the curves y=c/x and y=sin(x), where c is given by A196765.

%I A196766 #9 Mar 06 2021 01:56:00
%S A196766 4,4,2,1,2,0,5,9,2,9,5,4,9,9,8,3,9,1,3,3,5,6,1,6,2,4,4,0,5,0,4,7,6,1,
%T A196766 3,6,1,8,6,9,0,7,0,8,6,1,2,8,6,1,0,1,5,2,9,5,8,7,9,4,3,9,1,1,9,4,5,6,
%U A196766 6,6,5,7,9,4,5,8,7,2,6,2,5,7,9,6,8,0,2,6,6,6,0,0,1,7,6,8,9,5,3
%N A196766 Decimal expansion of the slope (negative) at the point of tangency of the curves y=c/x and y=sin(x), where c is given by A196765.
%e A196766 x=-0.44212059295499839133561624405047613618690708...
%t A196766 Plot[{Sin[x], 1/x, 1.82/x}, {x, 0, Pi}]
%t A196766 xt = x /. FindRoot[x + Tan[x] == 0, {x, 1.5, 2.5}, WorkingPrecision -> 100]
%t A196766 RealDigits[xt]   (* A196504 *)
%t A196766 c = N[xt*Sin[xt], 100]
%t A196766 RealDigits[c]    (* A196765 *)
%t A196766 slope = Cos[xt]
%t A196766 RealDigits[slope](* A196766 *)
%Y A196766 Cf. A196765.
%K A196766 nonn,cons
%O A196766 0,1
%A A196766 _Clark Kimberling_, Oct 06 2011