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Math Help - with floor functions

  1. #1
    Junior Member
    Joined
    Oct 2007
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    43

    with floor functions

    Show that the function:

    f(x) = \frac{x - \lfloor x \rfloor}{x + \lfloor x \rfloor +1} is:

    a) always upper-semicontinuous;
    b) has a derivative for all x belonging to N (natural numbers).

    Thanks in advance for the help all you mathwizzes out there.
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  2. #2
    Junior Member
    Joined
    Oct 2007
    Posts
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    sorry folks I made a terrible typing mistake.

    the question's part b should be:

    b) for all x not belonging to Z.
    And now that I come to think of it the solution is rather simple, so I take back the question to this part.

    However part a) is still puzzling me (and I'm sure there are no typos here) Any ideas?
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