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

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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