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

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

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

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

1

Solution steps

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

1 - x

is negative when

x \to 1 +

. Therefore

∣ 1 - x ∣ = - 1 + x

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

Simplify

= x \to 1 + lim (1)

x \to a lim c = c

= 1

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