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Lim x-> -2+ (x + 3) times [(absolute value (x + 2)) / (x + 2)]?

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and Lim x-> -2 - (x + 3) times [(absolute value (x + 2)) / (x + 2)]

Find the limits and explain how to get them please!

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  1. For x > -2, |x + 2| = (x+2)  Ã‚  (consider, for example, x = -1.99) Then

    (x+3) |x + 2| / (x+ 2) = (x+3)(x+2)/(x+2) = (x+3) for x ≠ -2.

    So

    lim (x+3) |x + 2| / (x+ 2) =

    x→-2+

    lim (x+3) = 1

    x→-2+

    In contrast, when x < -2, |x + 2| = -(x + 2)   (consider, for example, x = -2.01) Then

    (x+3) |x + 2| / (x+ 2) = (x+3)[-(x+2)]/(x+2) = -(x+3) for x ≠ -2.

    So

    lim (x+3) |x + 2| / (x+ 2) =

    x→-2-

    lim -(x+3) = -1

    x→-2-

You're reading: Lim x-> -2+ (x + 3) times [(absolute value (x + 2)) / (x + 2)]?

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