What is the limit as x approaches 3 of (|x-2|)/(x-2) ?

The limit as x approaches 3 of (|x-2|)/(x-2) is 1

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limit as x approaches 3 of (|x-2|)/(x-2)

x \to 3 lim (\frac{∣ x - 2 ∣}{x - 2})

1

Solution steps

x \to 3 lim (\frac{∣ x - 2 ∣}{x - 2})

Plug in the value

x = 3

= \frac{∣ 3 - 2 ∣}{3 - 2}

Simplify

\frac{∣ 3 - 2 ∣}{3 - 2} : 1

= 1

What is the limit as x approaches 3 of (|x-2|)/(x-2) ?
The limit as x approaches 3 of (|x-2|)/(x-2) is 1