What is the limit as x approaches 8-of (|x-8|)/(x-8) ?

The limit as x approaches 8-of (|x-8|)/(x-8) is -1

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limit as x approaches 8-of (|x-8|)/(x-8)

x \to 8 - lim (\frac{∣ x - 8 ∣}{x - 8})

- 1

Solution steps

x \to 8 - lim (\frac{∣ x - 8 ∣}{x - 8})

x - 8

is negative when

x \to 8 -

. Therefore

∣ x - 8 ∣ = - x + 8

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

\frac{- x + 8}{x - 8} = - 1

= x \to 8 - lim (- 1)

x \to a lim c = c

= - 1

What is the limit as x approaches 8-of (|x-8|)/(x-8) ?
The limit as x approaches 8-of (|x-8|)/(x-8) is -1