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Notation or whatever you want to call it!

  1. Dec 16, 2007 #1

    [tex]\lim_{x \rightarrow 0^+}|x|[/tex]

    [tex]x \geq 0[/tex]

    [tex]\lim_{x \rightarrow 0^-}|x|[/tex]

    [tex]x < 0[/tex]

    now for a similar limit, such as

    [tex]\lim_{x \rightarrow -4^+}|x+4|[/tex]

    the Domain is from

    [tex]x > -4[/tex]

    Why isn't it like |x|, whose Domain is greater than or equal to 0? Which in this case, greater than or equal to -4.
    Last edited: Dec 16, 2007
  2. jcsd
  3. Dec 17, 2007 #2

    Gib Z

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    Homework Helper

    What you typed doesn't really make much sense :( Really you just wrote some lines of tex and expected us to follow >.< They mean nothing on their own.
  4. Dec 17, 2007 #3


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    Staff Emeritus
    Science Advisor

    For [itex]x\ge 0[/itex] |x| is just x

    For [itex]x< 0[/itex] |x| is just -x

    Not unless it is specified to be that. The domain for |x+4|, just like the domain for |x| is "all real numbers". Of course |y| is y if [itex]y\ge 0[/itex], -y if y< 0. Letting y= x+4, |x+4|= x+4 if [itex]x+4\ge 0[/itex] which is the same as [itex]x\ge -4[/itex], and |x+4|= -(x+4) if x+4< 0 which is the same as x< -4. That's why it is convenient sometimes to restrict |x| to [itex]x\ge 4[/itex] or |x+4| to [itex]x\ge -4[/itex].
    Last edited: Dec 17, 2007
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