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calculus - limits

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can someone help me determine that limit for the following function, as x --> -2?

2 - abs(x) / 2 + x

  • calculus - limits - ,

    Please be sure to enclose numerators and denominators in parentheses when transcribing fractions. The given expression does not equal to
    (2-abs(x))/(2+x), which I will assume is the correct form.

    f(x) = (2-abs(x))/(2+x)
    is the same as
    f(x)=(2-x)/(2+x) when x∈[0,∞)
    f(x)=(2+x)/(2+x) when x∈(-∞,-2)∪(-2,0)

    As x→-2,
    f(x)=(2+x)/(2+x)
    which equals 1 by long division.
    Therefre
    Lim x→-2 f(x) = 1

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