cp's OEIS Frontend

A196915 Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/(1+x^2) and y=c*cos(x), where c is given by A196914.

%I A196915 #9 Mar 06 2021 02:01:50
%S A196915 6,0,7,6,2,2,2,3,7,6,9,6,8,6,8,6,5,8,5,9,0,0,1,0,0,2,6,8,2,0,2,6,3,6,
%T A196915 4,3,2,2,7,4,8,0,9,8,7,7,7,6,5,9,7,7,8,9,9,8,2,6,0,9,5,9,6,0,2,6,2,7,
%U A196915 3,3,6,3,0,4,6,2,8,4,7,5,8,1,4,8,2,6,6,5,4,7,4,8,5,6,0,2,5,6,6
%N A196915 Decimal expansion of the slope (negative) at the point of tangency of the curves y=1/(1+x^2) and y=c*cos(x), where c is given by A196914.
%e A196915 x=-0.60762223769686865859001002682026364322748...
%t A196915 Plot[{1/(1 + x^2), 0.874*Cos[x]}, {x, .5, 1}]
%t A196915 t = x /. FindRoot[Tan[x] == 2 x/(1 + x^2), {x, .5, 1}, WorkingPrecision -> 100]
%t A196915 RealDigits[t]     (* A196913 *)
%t A196915 c = N[Sqrt[t^4 + 6 t^2 + 1]/(t^4 + 2 t^2 + 1), 100]
%t A196915 RealDigits[c]     (* A196914 *)
%t A196915 slope = N[-c*Sin[t], 100]
%t A196915 RealDigits[slope] (* A196915 *)
%Y A196915 Cf. A196914, A196913.
%K A196915 nonn,cons
%O A196915 0,1
%A A196915 _Clark Kimberling_, Oct 07 2011