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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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Messages In This Thread
a curious limit - by JmsNxn - 04/14/2011, 08:01 PM
RE: a curious limit - by nuninho1980 - 04/14/2011, 08:10 PM
RE: a curious limit - by JmsNxn - 04/14/2011, 08:21 PM
RE: a curious limit - by bo198214 - 04/14/2011, 10:14 PM
RE: a curious limit - by JmsNxn - 04/14/2011, 10:55 PM
RE: a curious limit - by bo198214 - 04/15/2011, 07:14 AM
RE: a curious limit - by JmsNxn - 04/15/2011, 05:09 PM
RE: a curious limit - by JmsNxn - 04/16/2011, 07:22 PM
RE: a curious limit - by bo198214 - 04/16/2011, 07:41 PM
RE: a curious limit - by JmsNxn - 04/16/2011, 07:48 PM
RE: a curious limit - by bo198214 - 04/16/2011, 08:19 PM

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