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 negative when

x \to 1 -

. Therefore

∣ x - 1 ∣ = - x + 1

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

Simplify

= x \to 1 - lim (1)

x \to a lim c = c

= 1

y = 8 e^{8 e^{x} + x}

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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