What is the limit as x approaches 7-of (x-7)/(|x-7|) ?

The limit as x approaches 7-of (x-7)/(|x-7|) is -1

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limit as x approaches 7-of (x-7)/(|x-7|)

x \to 7 - lim (\frac{x - 7}{∣ x - 7 ∣})

- 1

Solution steps

x \to 7 - lim (\frac{x - 7}{∣ x - 7 ∣})

x - 7

is negative when

x \to 7 -

. Therefore

∣ x - 7 ∣ = - x + 7

= x \to 7 - lim (\frac{x - 7}{- x + 7})

\frac{x - 7}{- x + 7} = - 1

= x \to 7 - lim (- 1)

x \to a lim c = c

= - 1

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What is the limit as x approaches 7-of (x-7)/(|x-7|) ?
The limit as x approaches 7-of (x-7)/(|x-7|) is -1