What is the limit as x approaches 2 of (|x-2|)/x+6 ?

The limit as x approaches 2 of (|x-2|)/x+6 is 6

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limit as x approaches 2 of (|x-2|)/x+6

x \to 2 lim (\frac{∣ x - 2 ∣}{x} + 6)

6

Solution steps

x \to 2 lim (\frac{∣ x - 2 ∣}{x} + 6)

Plug in the value

x = 2

= \frac{∣ 2 - 2 ∣}{2} + 6

Simplify

\frac{∣ 2 - 2 ∣}{2} + 6 : 6

= 6

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What is the limit as x approaches 2 of (|x-2|)/x+6 ?
The limit as x approaches 2 of (|x-2|)/x+6 is 6