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a curious limit
#11
But if we are going back to the original question, and I set now , whether
converges, for , one would derive:

This implies several things (assuming a>0):
  1. b=0, i.e. then you have the limit 0
  2. if b>0, and you wind around anti-clockwise (incresing ) approaching 0, then you have limit 0. Note that you must put the log-cut accordingly (spiralling) that it allows increasing
  3. if b<0, then as above but clockwise (decreasing )
  4. if b>0 and you wind around slow enough but clockwise, you may also have a limit. I.e. faster than
  5. opposite of the previous

So you see, it really depends on how you approach 0.
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