What is the limit as x approaches 4-of (|x-4|)/(x-4) ?

The limit as x approaches 4-of (|x-4|)/(x-4) is -1

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limit as x approaches 4-of (|x-4|)/(x-4)

x \to 4 - lim (\frac{∣ x - 4 ∣}{x - 4})

- 1

Solution steps

x \to 4 - lim (\frac{∣ x - 4 ∣}{x - 4})

x - 4

is negative when

x \to 4 -

. Therefore

∣ x - 4 ∣ = - x + 4

= x \to 4 - lim (\frac{- x + 4}{x - 4})

\frac{- x + 4}{x - 4} = - 1

= x \to 4 - lim (- 1)

x \to a lim c = c

= - 1

What is the limit as x approaches 4-of (|x-4|)/(x-4) ?
The limit as x approaches 4-of (|x-4|)/(x-4) is -1