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

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

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

x \to 2 lim (\frac{∣ x - 1 ∣}{x - 1})

1

Solution steps

x \to 2 lim (\frac{∣ x - 1 ∣}{x - 1})

Plug in the value

x = 2

= \frac{∣ 2 - 1 ∣}{2 - 1}

Simplify

\frac{∣ 2 - 1 ∣}{2 - 1} : 1

= 1

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