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Math Help - Absolute value limits

  1. #1
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    Absolute value limits

    Can someone please refresh my memory as to how I'd solve down on an equation as such? I seem to be quite foggy with pre-calc. :/

    lim x->2
    |x-2|
    ____________________
    x-2

    _______= divided by. :P
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  2. #2
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    Quote Originally Posted by jimmyp View Post
    Can someone please refresh my memory as to how I'd solve down on an equation as such? I seem to be quite foggy with pre-calc. :/

    lim x->2
    |x-2|
    ____________________
    x-2

    _______= divided by. :P

    If you mean

    \lim_{x \to 2}\frac{|x-2|}{x-2}

    This limit does not exist.

    The limit from the left is

    \lim_{x \to 2^-}\frac{2-x}{x-2}=-1

    The limit from the right is

    \lim_{x \to 2^+}\frac{x-2}{x-2}=1

    Since the left and right limits are not equal the limit does not exist.
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