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

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

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

z \to 0 lim (\frac{∣ x ∣ - z}{z})

diverges

Solution steps

z \to 0 lim (\frac{∣ x ∣ - z}{z})

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

then the limit does not exist

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

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

= diverges

x \to \infty lim (- x + 3)

x \to - \infty lim (x^{3} - 4 x)

x \to 0 + lim (\frac{- 1}{x ^{2}})

x \to - 1 lim ((- 1)^{x} 2^{- x})

x \to 5 - lim (\frac{2 x}{x - 5})

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