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

The limit as x approaches 2 of (|x-2|)/x is 0

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

x \to 2 lim (\frac{∣ x - 2 ∣}{x})

0

Solution steps

x \to 2 lim (\frac{∣ x - 2 ∣}{x})

Plug in the value

x = 2

= \frac{∣ 2 - 2 ∣}{2}

Simplify

\frac{∣ 2 - 2 ∣}{2} : 0

= 0

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What is the limit as x approaches 2 of (|x-2|)/x ?
The limit as x approaches 2 of (|x-2|)/x is 0