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

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

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

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

- 1

Solution steps

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

2 - x

is negative when

x \to 2 +

. Therefore

∣ 2 - x ∣ = - 2 + x

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

\frac{- 2 + x}{2 - x} = - 1

= x \to 2 + lim (- 1)

x \to a lim c = c

= - 1

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