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

The limit as x approaches 0+of (|x-0|)/(0-x) is -1

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

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

- 1

Solution steps

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

x - 0

is positive when

x \to 0 +

. Therefore

∣ x - 0 ∣ = x - 0

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

Simplify

= x \to 0 + lim (- 1)

x \to a lim c = c

= - 1

What is the limit as x approaches 0+of (|x-0|)/(0-x) ?
The limit as x approaches 0+of (|x-0|)/(0-x) is -1