cp's OEIS Frontend

A196824 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 A196774.

%I A196824 #12 Aug 10 2021 16:32:15
%S A196824 6,3,4,1,6,4,9,7,0,6,9,5,8,7,7,9,5,6,1,0,2,7,4,9,8,1,1,8,6,4,0,2,3,8,
%T A196824 0,5,5,8,2,2,4,8,4,2,8,3,9,3,2,7,5,4,5,8,4,2,1,3,3,1,7,4,7,4,1,0,3,6,
%U A196824 3,6,2,9,9,4,1,7,8,8,6,3,1,0,0,1,9,3,6,4,8,0,6,5,8,7,6,8,4,6,6,7,1,4,5,6,8,1
%N A196824 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 A196774.
%e A196824 slope=-0.6341649706958779561027498118640238055822484...
%t A196824 Plot[{1/(1 + x^2), -.094 + Cos[x]}, {x, 0, 1}]
%t A196824 t = x /. FindRoot[2 x == ((1 + x^2)^2) Sin[x], {x, .5, 1}, WorkingPrecision -> 100]
%t A196824 RealDigits[t]     (* A196822 *)
%t A196824 c = N[-Cos[t] + 1/(1 + t^2), 100]
%t A196824 RealDigits[c]     (* A196823 *)
%t A196824 slope = N[-Sin[t], 100]
%t A196824 RealDigits[slope] (* A196824 *)
%Y A196824 Cf. A196823.
%K A196824 nonn,cons
%O A196824 0,1
%A A196824 _Clark Kimberling_, Oct 06 2011