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Limit question

  1. Sep 26, 2004 #1
    Hello all,

    I have a question that got me stumped.

    lim Sin x/|x|
    x->0

    The above limit. Does it exist or not? If yes why, and if no why not.

    Any help would be greatly appreciated :-)

    Thanks,
    Xargon
     
  2. jcsd
  3. Sep 26, 2004 #2

    Hurkyl

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    Staff Emeritus
    Science Advisor
    Gold Member

    Have you tried anything?

    Often a good approach when dealing with absolute values is to break the problem into two parts: one where the inside is positive and one where it is negative.
     
  4. Sep 26, 2004 #3
    Remember that one of the requirements for a limit to exist is the limit must be the same from both sides.

    Since 0/0 is undefined, you'll want to try x plus or minus some very small amount.

    For example, try .001 for x to determine the limit from the right. Then try -.001 to determine the limit from the left. See if they match up.
     
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