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

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

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

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

- 1

Solution steps

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

4 - x

is negative when

x \to 4 +

. Therefore

∣ 4 - x ∣ = - 4 + x

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

\frac{4 - x}{- 4 + x} = - 1

= x \to 4 + lim (- 1)

x \to a lim c = c

= - 1

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