What is the limit as x approaches 6-of (|x-6|)/(x-6) ?

The limit as x approaches 6-of (|x-6|)/(x-6) is -1

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limit as x approaches 6-of (|x-6|)/(x-6)

x \to 6 - lim (\frac{∣ x - 6 ∣}{x - 6})

- 1

Solution steps

x \to 6 - lim (\frac{∣ x - 6 ∣}{x - 6})

x - 6

is negative when

x \to 6 -

. Therefore

∣ x - 6 ∣ = - x + 6

= x \to 6 - lim (\frac{- x + 6}{x - 6})

\frac{- x + 6}{x - 6} = - 1

= x \to 6 - lim (- 1)

x \to a lim c = c

= - 1

What is the limit as x approaches 6-of (|x-6|)/(x-6) ?
The limit as x approaches 6-of (|x-6|)/(x-6) is -1