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

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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