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

The limit as x approaches 0 of (x-2)/(|x|-2) is 1

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

x \to 0 lim (\frac{x - 2}{∣ x ∣ - 2})

1

Solution steps

x \to 0 lim (\frac{x - 2}{∣ x ∣ - 2})

Plug in the value

x = 0

= \frac{0 - 2}{∣ 0 ∣ - 2}

Simplify

\frac{0 - 2}{∣ 0 ∣ - 2} : 1

= 1

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What is the limit as x approaches 0 of (x-2)/(|x|-2) ?
The limit as x approaches 0 of (x-2)/(|x|-2) is 1