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A196759 Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/x and y=c*sin(x), where c is given by A196758.

%I A196759 #10 Mar 06 2021 01:55:33
%S A196759 2,4,2,9,6,2,6,8,5,0,9,5,0,3,4,0,8,6,9,1,2,6,1,1,5,8,0,7,9,5,1,2,3,0,
%T A196759 7,3,0,1,2,2,6,9,4,4,5,7,7,8,0,1,5,6,2,1,4,8,8,6,0,3,9,0,7,9,6,1,2,1,
%U A196759 9,6,3,4,1,9,9,6,2,3,0,1,4,0,8,6,3,3,5,1,0,5,3,7,7,4,7,9,2,5,1,6
%N A196759 Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/x and y=c*sin(x), where c is given by A196758.
%e A196759 x=-0.242962685095034086912611580795123073012...
%t A196759 Plot[{1/x, .55*Sin[x]}, {x, 0, Pi}]
%t A196759 xt = x /. FindRoot[x + Tan[x] == 0, {x, 1.5, 2.5}, WorkingPrecision -> 100]
%t A196759 RealDigits[xt] (* A196504 *)
%t A196759 c = N[1/(xt*Sin[xt]), 100]
%t A196759 RealDigits[c]  (* A196758 *)
%t A196759 slope = -1/xt^2
%t A196759 RealDigits[slope]  (* A196759 *)
%Y A196759 Cf. A196758.
%K A196759 nonn,cons
%O A196759 0,1
%A A196759 _Clark Kimberling_, Oct 06 2011