What is the limit as x approaches-2 of (x-2)/(|x-2|) ?

The limit as x approaches-2 of (x-2)/(|x-2|) is -1

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limit as x approaches-2 of (x-2)/(|x-2|)

x \to - 2 lim (\frac{x - 2}{∣ x - 2 ∣})

- 1

Solution steps

x \to - 2 lim (\frac{x - 2}{∣ x - 2 ∣})

Plug in the value

x = - 2

= \frac{- 2 - 2}{∣ - 2 - 2 ∣}

Simplify

\frac{- 2 - 2}{∣ - 2 - 2 ∣} : - 1

= - 1

What is the limit as x approaches-2 of (x-2)/(|x-2|) ?
The limit as x approaches-2 of (x-2)/(|x-2|) is -1