What is the limit as x approaches 1-of 3/(|x-1|) ?

The limit as x approaches 1-of 3/(|x-1|) is infinity

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limit as x approaches 1-of 3/(|x-1|)

x \to 1 - lim (\frac{3}{∣ x - 1 ∣})

\infty

Solution steps

x \to 1 - lim (\frac{3}{∣ x - 1 ∣})

For

x

approaching

1

from the left

, x < 1 \Rightarrow ∣ x - 1 ∣ > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

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What is the limit as x approaches 1-of 3/(|x-1|) ?
The limit as x approaches 1-of 3/(|x-1|) is infinity