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

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

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

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

- 1

Solution steps

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

3 - x

is positive when

x \to 3 -

. Therefore

∣ 3 - x ∣ = 3 - x

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

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

= x \to 3 - lim (- 1)

x \to a lim c = c

= - 1

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