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

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

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

x \to 1 lim (\frac{1}{∣ x - 1 ∣})

\infty

Solution steps

x \to 1 lim (\frac{1}{∣ x - 1 ∣})

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

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

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

= \infty

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