What is the limit as x approaches 2 of (|x-1|)/(x-1) ?

The limit as x approaches 2 of (|x-1|)/(x-1) is 1

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limit as x approaches 2 of (|x-1|)/(x-1)

x \to 2 lim (\frac{∣ x - 1 ∣}{x - 1})

1

Solution steps

x \to 2 lim (\frac{∣ x - 1 ∣}{x - 1})

Plug in the value

x = 2

= \frac{∣ 2 - 1 ∣}{2 - 1}

Simplify

\frac{∣ 2 - 1 ∣}{2 - 1} : 1

= 1

x \to 0 lim (\frac{x}{( x + 3 ) ^{2} - 9})

x \to \frac{3 π}{4} lim (2 cos (x))

x \to 101 lim (\frac{x}{x + 4})

x \to 2 + lim (\frac{x + 1}{3 x - 6})

x \to (- 2) - lim (\frac{1}{x + 2})

What is the limit as x approaches 2 of (|x-1|)/(x-1) ?
The limit as x approaches 2 of (|x-1|)/(x-1) is 1