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Thread: Limits

  1. January 29th 2009, 02:17 AM #1
    CalcQueen
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    Limits

    Let f(x) = 5-x^2, x is less than or equal to 2
    (x+3)/(x-2), x>2

    Find the limit of f(x) as

    a) x approaches negative infinity
    b) x approaches 2^-
    c) x approaches 2^+
    d) x approaches positive infinity
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  2. January 29th 2009, 04:33 AM #2
    Soroban
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    Hello, CalcQueen!

    Let f(x) \:= \:\begin{Bmatrix}5-x^2& & x \leq 2 \\ \\[-4mm]\dfrac{x+3}{x-2}& & x>2 \end{Bmatrix}

    Find the limit of f(x) as:

    a)\;\;x \to -\infty
    \lim_{x\,\to\,\text{-}\infty}(5-x^2) \;=\;-\infty



    b)\;\;x \to 2^-
    \lim_{x\to2^-}(5-x^2) \;=\;1



    c)\;\; x \to 2^+

    \lim_{x\to2^+}\,\frac{x+3}{x-2} \;\to\;\frac{5}{0} \:\to\: \infty



    d)\;\;x \to +\infty

    \lim_{x\to2^+}\,\frac{x+3}{x-2} \;=\;\lim_{x\to2^+}\,\frac{1 + \frac{3}{x}}{1 - \frac{2}{x}} \;=\;\frac{1+0}{1-0} \:=\:1
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