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})

x

is positive when

x \to 2

. Therefore

∣ x ∣ = x

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

Simplify

= 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