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.

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, 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, 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

Offset: 0

Author

Clark Kimberling, Oct 07 2011

Keywords

• nonn
• cons

Examples

			x=-0.60762223769686865859001002682026364322748...
		

Crossrefs

Cf. A196914, A196913.

Programs

Mathematica

Plot[{1/(1 + x^2), 0.874*Cos[x]}, {x, .5, 1}]
t = x /. FindRoot[Tan[x] == 2 x/(1 + x^2), {x, .5, 1}, WorkingPrecision -> 100]
RealDigits[t]     (* A196913 *)
c = N[Sqrt[t^4 + 6 t^2 + 1]/(t^4 + 2 t^2 + 1), 100]
RealDigits[c]     (* A196914 *)
slope = N[-c*Sin[t], 100]
RealDigits[slope] (* A196915 *)