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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

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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]