A196611 Decimal expansion of the slope (negative) of the tangent line at the point of tangency of the curves y=c*cos(x) and y=1/x, where c is given by A196610.

1, 3, 5, 1, 0, 3, 3, 8, 8, 6, 8, 7, 8, 3, 7, 8, 6, 2, 4, 0, 0, 9, 1, 9, 2, 4, 7, 3, 5, 2, 8, 4, 3, 0, 2, 1, 7, 4, 8, 3, 4, 3, 7, 8, 0, 5, 9, 6, 3, 4, 7, 8, 1, 5, 9, 2, 3, 0, 1, 4, 5, 2, 3, 3, 6, 5, 4, 5, 9, 5, 8, 9, 8, 3, 5, 7, 6, 8, 7, 7, 2, 4, 9, 2, 4, 5, 3, 5, 7, 8, 7, 6, 5, 3, 0, 2, 9, 4, 9, 4

Offset: 1

Author

Clark Kimberling, Oct 04 2011

Keywords

• nonn
• cons

Comments

For x>0, there is exactly one number c for which the graphs of y=c*cos(x) and y=1/x, where 0

Examples

			slope = -1.3510338868783786240091924735284302174...
		

Crossrefs

Cf. A196610, A196603.

Programs

Mathematica

Plot[{1/x, (1.78222) Cos[x]}, {x, .7, 1}]
xt = x /. FindRoot[x == Cot[x], {x, .8, 1}, WorkingPrecision -> 100]
c = N[Csc[xt]/xt^2, 100]
RealDigits[c]  (* A196610 *)
slope = -c*Sin[xt]
RealDigits[slope]  (* A196611 *)

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