What is the limit as x approaches 4+of (x-4)/(|x-4|) ?

The limit as x approaches 4+of (x-4)/(|x-4|) is 1

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limit as x approaches 4+of (x-4)/(|x-4|)

x \to 4 + lim (\frac{x - 4}{∣ x - 4 ∣})

1

Solution steps

x \to 4 + lim (\frac{x - 4}{∣ x - 4 ∣})

x - 4

is positive when

x \to 4 +

. Therefore

∣ x - 4 ∣ = x - 4

= x \to 4 + lim (\frac{x - 4}{x - 4})

Simplify

= x \to 4 + lim (1)

x \to a lim c = c

= 1

x \to 0 lim (\frac{sin ^{2} ( x )}{x})

\frac{d}{d x} (ln (\frac{∣ x - 1 ∣}{∣ x - 3 ∣}))

\int 2 x sec^{2} (3 x) x d x

x \to 1 + lim (\frac{4 x}{2 x - 2})

x \to 0 lim (g (x) sin (\frac{1}{x}))

What is the limit as x approaches 4+of (x-4)/(|x-4|) ?
The limit as x approaches 4+of (x-4)/(|x-4|) is 1