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

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

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

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

1

Solution steps

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

x - 1

is positive when

x \to 1 +

. Therefore

∣ x - 1 ∣ = x - 1

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

Simplify

= x \to 1 + lim (1)

x \to a lim c = c

= 1

2 sec (x) tan (x)

\int cot^{2} (θ) csc (θ) d θ

\frac{s - 1}{( s + 1 ) ( s ^{2} + 1 )}

f (x) = \frac{x - 8}{3 x - 4}, at x = 2

\frac{d}{d x} (cos (x z (x)))

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