What is the limit as x approaches-4+of (x+4)/(|x+4|) ?

The limit as x approaches-4+of (x+4)/(|x+4|) is 1

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limit as x approaches-4+of (x+4)/(|x+4|)

x \to - 4 + lim (\frac{x + 4}{∣ x + 4 ∣})

1

Solution steps

x \to - 4 + lim (\frac{x + 4}{∣ x + 4 ∣})

x + 4

is positive when

x \to - 4 +

. Therefore

∣ x + 4 ∣ = x + 4

= x \to - 4 + lim (\frac{x + 4}{x + 4})

Simplify

= x \to - 4 + lim (1)

x \to a lim c = c

= 1

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What is the limit as x approaches-4+of (x+4)/(|x+4|) ?
The limit as x approaches-4+of (x+4)/(|x+4|) is 1