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Homework Help: Limit x->o- |x|

  1. Sep 16, 2011 #1
    1. The problem statement, all variables and given/known data
    the answer to this question [limit x->0- |x|] given to me by my instructor was -1. (by 0- i mean to say the left handed limit). i have been thinking for the last 15 minutes but could not understand it.

    i think the answer should be 0 because as we get closer to zero from the left side the distance between 0 and our number gets smaller and smaller till finally it approaches 0 itself.

    and as for the right hand limit of same question ( limit x->0+ |x|) i was given the answer 0 and that seems corret to me.
    so anyone please explain this..
  2. jcsd
  3. Sep 16, 2011 #2


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    Staff Emeritus
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    You are correct, the limit of |x| as x [itex]\to[/itex] 0 exists and is 0.

    [tex]\lim_{x\to0^-} |x| = \lim_{x\to0^+} |x| = \lim_{x\to0} |x| = 0[/tex]

    Perhaps it was a typo in your instructor's answer.
  4. Sep 16, 2011 #3


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    Or perhaps the problem was intended to be
    [tex]\lim_{x\to 0^-} \frac{|x|}{x}[/tex]
  5. Sep 16, 2011 #4
    Since you're approaching from the left what you're dealing with is a negative number and absolute value goes out as ( - x ) but x=0 so - x = - 0 = Zero
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