What is the limit as x approaches 3 of (|x-1|)/(x-1) ?

The limit as x approaches 3 of (|x-1|)/(x-1) is 1

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limit as x approaches 3 of (|x-1|)/(x-1)

x \to 3 lim (\frac{∣ x - 1 ∣}{x - 1})

1

Solution steps

x \to 3 lim (\frac{∣ x - 1 ∣}{x - 1})

Plug in the value

x = 3

= \frac{∣ 3 - 1 ∣}{3 - 1}

Simplify

\frac{∣ 3 - 1 ∣}{3 - 1} : 1

= 1

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

\int \frac{e ^{x}}{( e ^{x} + 1 )} d x

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7 x^{2} + \frac{d y}{d x} (x^{3} + 6) = 0

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What is the limit as x approaches 3 of (|x-1|)/(x-1) ?
The limit as x approaches 3 of (|x-1|)/(x-1) is 1