What is the limit as x approaches-5-of (|5-x|)/(5-x) ?

The limit as x approaches-5-of (|5-x|)/(5-x) is 1

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limit as x approaches-5-of (|5-x|)/(5-x)

x \to - 5 - lim (\frac{∣ 5 - x ∣}{5 - x})

1

Solution steps

x \to - 5 - lim (\frac{∣ 5 - x ∣}{5 - x})

Plug in the value

x = - 5

= \frac{∣ 5 - ( - 5 ) ∣}{5 - ( - 5 )}

Simplify

\frac{∣ 5 - ( - 5 ) ∣}{5 - ( - 5 )} : 1

= 1

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What is the limit as x approaches-5-of (|5-x|)/(5-x) ?
The limit as x approaches-5-of (|5-x|)/(5-x) is 1