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How to check if this function is continuous

  1. Jun 2, 2014 #1
    Hello.
    The question is in the attached, together with my attempt. As you can see, I found the limit, but I don't know what each value means. If I have calculated the limits correctly, how do I know know if f(z) is continuous at 0 or not?
     

    Attached Files:

  2. jcsd
  3. Jun 2, 2014 #2

    benorin

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    You have two different answers for the limit along different paths so the limit does not exist, therefore f(z) is not continuous at z=0.
     
  4. Jun 2, 2014 #3
    So, if no.1 and no.2 both had +/-1 as limits, then the function would be continuous at 0?
     
  5. Jun 2, 2014 #4

    benorin

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    No, if one is positive 1 and the other is negative 1, they are still different and thus the limit d.n.e. So it's not continuous there.
     
  6. Jun 2, 2014 #5
    Got it, thanks! By the way, could you look at my thread entitled contour integral please?
     
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