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

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

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

x \to 0 lim (\frac{∣ x - 1 ∣ - 1}{x})

- 1

Solution steps

x \to 0 lim (\frac{∣ x - 1 ∣ - 1}{x})

x - 1

is negative when

x \to 0

. Therefore

∣ x - 1 ∣ = - x + 1

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

Simplify

= x \to 0 lim (- 1)

x \to a lim c = c

= - 1

x \to 0 + lim (a x^{x^{2}})

x \to 3 lim (4 x^{3} - 5 x^{2} + x - 8)

\int sec^{2} (x) - csc (x) cot (x) d x

x \to - 3 lim (f (x) x)

\int \frac{4 x}{16 - x ^{4}} d x

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