What is the limit as x approaches 0 of 5/x-5/(|x|) ?

The limit as x approaches 0 of 5/x-5/(|x|) is diverges

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limit as x approaches 0 of 5/x-5/(|x|)

x \to 0 lim (\frac{5}{x} - \frac{5}{∣ x ∣})

diverges

Solution steps

x \to 0 lim (\frac{5}{x} - \frac{5}{∣ x ∣})

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

then the limit does not exist

x \to 0 + lim (\frac{5}{x} - \frac{5}{∣ x ∣}) = 0

x \to 0 - lim (\frac{5}{x} - \frac{5}{∣ x ∣}) = - \infty

= diverges

f (x) = x, g (x) = x, [0, 2]

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What is the limit as x approaches 0 of 5/x-5/(|x|) ?
The limit as x approaches 0 of 5/x-5/(|x|) is diverges