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timofeeve [1]
3 years ago
15

Limitation of -4 to the left of the absolute value of x+4 divided by x+4

Mathematics
1 answer:
timama [110]3 years ago
7 0

I believe you're asking about the one-sided limit,

\displaystyle \lim_{x\to-4^-}\frac{|x+4|}{x+4}

Recall the definition of absolute value:

• |x| = x if x\ge0

• |x| = -x if x < 0

Since we're approaching -4 from the left, we're effectively focusing on a domain of x or x+4. So, by the definition above, we have |x+4| = -(x+4). Then in the limit, we have

\displaystyle \lim_{x\to-4^-}\frac{|x+4|}{x+4} = \lim_{x\to-4^-}\frac{-(x+4)}{x+4} = \lim_{x\to-4^-}(-1) = \boxed{-1}

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