What is the limit as x approaches 2-of (x-1)/(|x-1|) ?

The limit as x approaches 2-of (x-1)/(|x-1|) is 1

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limit as x approaches 2-of (x-1)/(|x-1|)

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

1

Solution steps

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

Plug in the value

x = 2

= \frac{2 - 1}{∣ 2 - 1 ∣}

Simplify

\frac{2 - 1}{∣ 2 - 1 ∣} : 1

= 1

\frac{d}{d x} (3 x^{3} y^{2})

\frac{d y}{d x} = \frac{2 x + sec ^{2} ( x )}{4 y}

\frac{\partial}{\partial y} (y ln (x))

\frac{d}{d x} (40 x^{4} + 180 x^{3} + 240 x^{2} + 100 x)

\frac{d}{d x} (\frac{1}{3} (3 - 5 x)^{3})

What is the limit as x approaches 2-of (x-1)/(|x-1|) ?
The limit as x approaches 2-of (x-1)/(|x-1|) is 1