determine infinite limits?

lim x+3/x+4 lim x+3/x+4

x approaches -4^- x approaches -4^+

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  • 9 years ago
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    lim (x + 3) / (x + 4) = (-4 + 3) / (-4 + 4) = -1/0 = ∞

    x----> -4 -

    the reason is + ∞ is if we can start plugging numbers such as coming from the left as -5 , -6

    when x = -6

    (-6 + 3) / (-6 + 4) = -3/-2 = 3/2 = 1.5

    when x = -5

    (-5 + 3) / (-5 + 4) = -2/-1 = 2

    so we are increasing.

    lim (x + 3) / (x + 4) = (-4 + 3) / (-4 + 4) = -1/0 = - ∞

    x----> -4 +

    the reason is - ∞ is if we can start plugging numbers such as coming from the right as -2 , -3

    when x = -2

    (-2 + 3) / (-2 + 4) = 1/2

    when x = -3

    (-3 + 3) / (-3 + 4) = 0/1 = 0

    so we are decreasing.

    RHS ≠ LHS which the lim DNE.

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