What is the limit as x approaches 9-of (|x-9|)/(x-9) ?

The limit as x approaches 9-of (|x-9|)/(x-9) is -1

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limit as x approaches 9-of (|x-9|)/(x-9)

x \to 9 - lim (\frac{∣ x - 9 ∣}{x - 9})

- 1

Solution steps

x \to 9 - lim (\frac{∣ x - 9 ∣}{x - 9})

x - 9

is negative when

x \to 9 -

. Therefore

∣ x - 9 ∣ = - x + 9

= x \to 9 - lim (\frac{- x + 9}{x - 9})

\frac{- x + 9}{x - 9} = - 1

= x \to 9 - lim (- 1)

x \to a lim c = c

= - 1

What is the limit as x approaches 9-of (|x-9|)/(x-9) ?
The limit as x approaches 9-of (|x-9|)/(x-9) is -1