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Limit of absolute value

  1. Sep 23, 2005 #1
    Is it correct that [itex]|\sin x|=-\sin x[/itex] as [itex]x\rightarrow 0-[/itex]?

    It's clear for a function like [itex]y=x[/itex], but I ask the question since the sine oscillates from positive to negative values, so for different x's the abs. value is either pos. or neg. Or do I only need to consider values of x that are between -pi and 0?

    I know the limit is zero, I just need to know how to write the intermediate step of getting rid of the abs. value sign.

    - Kamataat
  2. jcsd
  3. Sep 23, 2005 #2


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    If you're approaching 0 from the left (so bottom, smaller values i.e. negatives) then the sine is negative there, so |sinx| indeed becomes -sinx.
  4. Sep 23, 2005 #3
    Thanks for the quick reply!

    - Kamataat
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