What is the limit as x approaches-3-of (|x+3|)/(x+3) ?

The limit as x approaches-3-of (|x+3|)/(x+3) is -1

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limit as x approaches-3-of (|x+3|)/(x+3)

x \to - 3 - lim (\frac{∣ x + 3 ∣}{x + 3})

- 1

Solution steps

x \to - 3 - lim (\frac{∣ x + 3 ∣}{x + 3})

x + 3

is negative when

x \to - 3 -

. Therefore

∣ x + 3 ∣ = - x - 3

= x \to - 3 - lim (\frac{- x - 3}{x + 3})

\frac{- x - 3}{x + 3} = - 1

= x \to - 3 - lim (- 1)

x \to a lim c = c

= - 1

x \to - 8 - lim (\frac{x + 3}{x + 8})

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What is the limit as x approaches-3-of (|x+3|)/(x+3) ?
The limit as x approaches-3-of (|x+3|)/(x+3) is -1