

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.


2



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



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]
slope = c*Sin[xt]


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



