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Given two functions x[T],y[T]

x[T_] := (100000 T)/(47 Log[18/(-7 + 25 Abs[Cos[100 \[Pi] T]])])
y[T_] := 100 (-(7/500) + (7 T)/5 - (5 T (-1 + Abs[Cos[100 \[Pi] T]]))/Log[18/(-7 + 25 Abs[Cos[100 \[Pi] T]])] + Sin[100 \[Pi] T]/(20 \[Pi]))

the plot is easily created

Plot[{x[u], y[u]}, {u, .006, .01}]

enter image description here

If I try ParametricPlot (with adjusted PlotRange and AspectRatio) I get an empty plot

ParametricPlot[{x[u], y[u]}, {u, .006, .01},PlotRange -> {{0, 1500}, {0, 5}}, AspectRatio -> 1]

enter image description here

Any suggestions? Thanks!

remark:
Meanwhile I found a workaround by decreasing the plotintervall:

ParametricPlot[ {x[u], y[u]} , {u, .006, .01 - .001},AspectRatio -> 1] 

Knowing that u==0.01is Indeterminate unfortunately I can't exclude it:

ParametricPlot[ {x[u], y[u]} , {u, .006, .01  },AspectRatio ->1,Exclusions->{0.01}] 
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Enlarge PlotPoints or MaxRecursion, both yield the desired plot.

ParametricPlot[{x[u], y[u]}, {u, .006, .01}, 
   PlotRange -> {{0, 1500}, {0, 5}}, AspectRatio -> 1, 
   PlotPoints -> 500]

ParametricPlot[{x[u], y[u]}, {u, .006, .01}, 
   PlotRange -> {{0, 1500}, {0, 5}}, AspectRatio -> 1, 
   MaxRecursion -> 10]
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  • $\begingroup$ Thanks! I'm wondering whyMaxRecursion-> is needed in the ParametricPlot , but not in Plot? $\endgroup$ – Ulrich Neumann Jun 21 '18 at 7:41

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