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

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

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

x \to 2 + lim (\frac{x - 2}{∣ x - 2 ∣})

1

Solution steps

x \to 2 + lim (\frac{x - 2}{∣ x - 2 ∣})

x - 2

is positive when

x \to 2 +

. Therefore

∣ x - 2 ∣ = x - 2

= x \to 2 + lim (\frac{x - 2}{x - 2})

Simplify

= x \to 2 + lim (1)

x \to a lim c = c

= 1

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