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A196833 Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/(1+x^2) and y=c*sin(x), where c is given by A196832.

%I A196833 #9 Mar 06 2021 02:01:59
%S A196833 1,2,7,0,7,1,8,4,1,1,8,6,4,4,1,9,0,5,9,4,7,9,4,4,6,4,3,3,9,3,0,0,1,7,
%T A196833 6,8,3,8,5,6,2,5,4,4,7,1,6,6,1,6,1,6,3,2,0,7,5,0,6,4,5,8,1,2,0,3,8,7,
%U A196833 5,4,2,8,7,7,9,2,4,1,7,9,1,2,7,7,0,9,9,2,3,3,8,2,7,6,7,3,3,4,3,7
%N A196833 Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/(1+x^2) and y=c*sin(x), where c is given by A196832.
%e A196833 x=-0.12707184118644190594794464339300176838562544...
%t A196833 Plot[{1/(1 + x^2), .205 Sin[x]}, {x, 0, Pi}]
%t A196833 t = x /. FindRoot[x^2 + 2 x*Tan[x] + 1 == 0, {x, 2, 3}, WorkingPrecision -> 100]
%t A196833 RealDigits[t]     (* A196831 *)
%t A196833 c = N[Csc[t]/(1 + t^2), 100]
%t A196833 RealDigits[c]     (* A196832 *)
%t A196833 slope = N[c*Cos[t], 100]
%t A196833 RealDigits[slope] (* A196833 *)
%Y A196833 Cf. A196825, A196832.
%K A196833 nonn,cons
%O A196833 0,2
%A A196833 _Clark Kimberling_, Oct 07 2011