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

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

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

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

1

Solution steps

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

Plug in the value

x = 3

= \frac{3 - 1}{3 - 1}

Simplify

\frac{3 - 1}{3 - 1} : 1

= 1

x \to 4 lim (\frac{x ^{2} - 6}{x + 2})

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

x \to 31 lim (31 - x)

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

x \to 39 lim (- x^{2} + 2 x + 1)

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