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

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

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

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

1

Solution steps

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

\frac{x - 3}{x - 3}

is positive when

x \to 3 -

. Therefore

\frac{x - 3}{x - 3} = \frac{x - 3}{x - 3}

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

Simplify

= x \to 3 - lim (1)

x \to a lim c = c

= 1

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