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

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

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

x \to 1 lim (\frac{∣ x - 3 ∣}{x - 3})

- 1

Solution steps

x \to 1 lim (\frac{∣ x - 3 ∣}{x - 3})

Plug in the value

x = 1

= \frac{∣ 1 - 3 ∣}{1 - 3}

Simplify

\frac{∣ 1 - 3 ∣}{1 - 3} : - 1

= - 1

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