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Differantiation proof question

  1. Jan 25, 2009 #1
    here is the question and how i tried to solve it??

    [​IMG]
     
  2. jcsd
  3. Jan 26, 2009 #2

    Gib Z

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    Well good, you got quite far. Look at where your limits got you to. You can take out the [tex]\phi (x)[/tex] out from the limits now can't you? Your remaining limit, what does that approach from the left? How about from the right?
     
    Last edited: Jan 26, 2009
  4. Jan 26, 2009 #3
    i cant take out
    [tex]\phi (x)[/tex]

    out of the limit .
    its not a constant
    ??
     
  5. Jan 26, 2009 #4

    Gib Z

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    Well really it doesn't matter whether you leave it in there or not, its still easy to see that we get different limits from the left and right just by considering the other things in the limit. But we can take it out of the limit because we can regard it as a constant with respect to the limiting variable.
     
  6. Jan 28, 2009 #5
    i cant see
    how we get different results

    there is another function inside
    i dont know how to get a result
    ??
     
  7. Jan 28, 2009 #6

    Gib Z

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    Consider

    [tex]\lim_{x\to 0} \frac{ |x| }{x}[/tex]. What is it from the left? How about right? So it does exist?
     
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