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Math Help - One sided limit

  1. #1
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    One sided limit

    Hello i still have a problem about graphing absolute values:
    Sketch the graph of the function and find the indicated limit if it exists; if the limit does not exist, state the reason:
    G(x) = |2x - 3| - 4
    find:
    a.) \lim_{x \to {\frac{3}{2}}^+}
    b.) \lim_{x \to {\frac{3}{2}}^-}
    c.) \lim_{x \to {\frac{3}{2}}}<--- does it exist?

    Thanks and
    Happy holidays!
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  2. #2
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    The limit exists

    The limit exists because a = -4 and b = -4 are the same
    nevmind
    my problem is only the graphing the absolute value
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  3. #3
    Forum Admin topsquark's Avatar
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    First look at where the absolute value portion of the function is 0:
    2x - 3 = 0

    x = -\frac{3}{2}

    Now split the function into two pieces:
    G(x) = \left \{ \begin{array}{cc} -(2x-3)-4 & x < -\frac{3}{2} \\ (2x-3) - 4 & x \geq -\frac{3}{2} \end{array} \right .

    -Dan
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