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.

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, 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, 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

Offset: 0

Author

Clark Kimberling, Oct 07 2011

Keywords

• nonn
• cons

Examples

			x=-0.12707184118644190594794464339300176838562544...
		

Crossrefs

Cf. A196825, A196832.

Programs

Mathematica

Plot[{1/(1 + x^2), .205 Sin[x]}, {x, 0, Pi}]
t = x /. FindRoot[x^2 + 2 x*Tan[x] + 1 == 0, {x, 2, 3}, WorkingPrecision -> 100]
RealDigits[t]     (* A196831 *)
c = N[Csc[t]/(1 + t^2), 100]
RealDigits[c]     (* A196832 *)
slope = N[c*Cos[t], 100]
RealDigits[slope] (* A196833 *)