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

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

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

x \to 1 + lim (\frac{∣ x - 1 ∣}{1 - x})

- 1

Solution steps

x \to 1 + lim (\frac{∣ x - 1 ∣}{1 - x})

x - 1

is positive when

x \to 1 +

. Therefore

∣ x - 1 ∣ = x - 1

= x \to 1 + lim (\frac{x - 1}{1 - x})

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

= x \to 1 + lim (- 1)

x \to a lim c = c

= - 1

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