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

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

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

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

1

Solution steps

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

1 - x

is positive when

x \to 1 -

. Therefore

∣ 1 - x ∣ = 1 - x

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

Simplify

= x \to 1 - lim (1)

x \to a lim c = c

= 1

x \to 0 + lim ((1 - 9 x)^{\frac{9}{x}})

x \to - 4 lim (sin (- π x))

x \to \infty lim (\frac{ln ( \infty )}{\infty})

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

x \to 0 lim (sin (x - 1))

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