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Limits of Complex funtions

  1. Jul 28, 2008 #1
    Hey ppl....

    Is x/x differentiable at x = 0

    Now i know that it is not defined at x=0 but the function does approach the same limits from either side...From what i remember the limit does exist (what was the name of the rule that lets you do that)...but does that mean it is differentiable at x= 0 ???

    Also can the same idea be extended to complex functions (say z/z)

    Thanks in advance
     
  2. jcsd
  3. Jul 28, 2008 #2

    HallsofIvy

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    x/x??

    As you say, that is not defined at x= 0 and so cannot be continuous or differentiable there.

    Of course, it has a "removable" discontinuity at x= 0. For all x other than 0, x/x= 1 so the limit, as x goes to 0, is 1. We can make this function continous at x= 0 by defining it to be 1 there. In that case, we just have the function f(x)= 1 for all x. It's derivative is the constant 0.

    But what does this have to do with complex numbers? Did you mean to ask about z/|z| ? That would be a much more interesting question!
     
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