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 positive when

x \to 4 -

. Therefore

∣ 4 - x ∣ = 4 - x

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

Simplify

= 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