A parametric equation, say(adsbygoogle = window.adsbygoogle || []).push({}); , is smoothly parametrized if:r(t)

1. its derivative is continuous, and

2. its derivative does not equal zero for all t in the domain of r.

Now that sounds simple enough. Now lets say we have thetractrix:

, ...r(t) = (t-tanht)i + sechtj

then, right?r'(t) = [ 1/(1+x^2) ]i + [ tantsect ]j

Now, without reverting to MatLab or Maple to view the graph, how do we mathematically explain thatis continuous (or not)?r'(t)

Do I just state that is is/isn't -by inspection, or ...?

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# How to show a parametric equation is continuous?

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