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Math Help - [SOLVED] limits

  1. #1
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    [SOLVED] limits

    why does lim (x/|x|) = 1
    x-> 0+
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by ricey View Post
    why does lim (x/|x|) = 1
    x-> 0+
    It does because we are only concerned about the behavior of the graph from the right, IE: (positive values of x)

    Note how any positive number divided by the absolute value of that number will always be positve 1.

    Since |x|=\left\{\begin{array}{cc}{-x},&\mbox{ if }{x}\leq0\\x,&\mbox{ if }{x>0}\end{array}\right.

    Then for values greater than 0, we have \frac{x}{|x|}=\frac{x}{x}

    Therefore \lim_{x\to0^+}\frac{x}{|x|}=\lim_{x\to0^+}\frac{x}  {x}=\lim_{x\to0^+}(1)=1.
    Last edited by VonNemo19; July 28th 2009 at 08:43 PM.
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  3. #3
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    okay i get it! Thanks so much
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