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

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

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limit as x approaches 1 of (|x-1|-|x|)/x

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

- 1

Solution steps

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

Plug in the value

x = 1

= \frac{∣ 1 - 1 ∣ - ∣ 1 ∣}{1}

Simplify

\frac{∣ 1 - 1 ∣ - ∣ 1 ∣}{1} : - 1

= - 1

x \to - 7 lim (x^{2} + 8)

x \to 0 lim (\frac{x - 2}{3 x})

x \to - 1 lim (\frac{3 x}{2 x + 2})

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

x \to 0 lim (\frac{5 ^{x}}{x})

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