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

1,2

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<x<2*Pi, have the same tangent line.

Links

Table of n, a(n) for n=1..100.

Example

slope = -1.3510338868783786240091924735284302174...

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 *)

Crossrefs

Cf. A196610, A196603.

Sequence in context: A146525 A394453 A395843 * A011353 A016452 A346095

Adjacent sequences: A196608 A196609 A196610 * A196612 A196613 A196614

Keyword

nonn,cons

Author

Clark Kimberling, Oct 04 2011

Status

approved