What is the limit as x approaches 5 of (|x-5|)/(x-5) ?

The limit as x approaches 5 of (|x-5|)/(x-5) is diverges

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limit as x approaches 5 of (|x-5|)/(x-5)

x \to 5 lim (\frac{∣ x - 5 ∣}{x - 5})

diverges

Solution steps

x \to 5 lim (\frac{∣ x - 5 ∣}{x - 5})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 5 + lim (\frac{∣ x - 5 ∣}{x - 5}) = 1

x \to 5 - lim (\frac{∣ x - 5 ∣}{x - 5}) = - 1

= diverges

What is the limit as x approaches 5 of (|x-5|)/(x-5) ?
The limit as x approaches 5 of (|x-5|)/(x-5) is diverges