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 positive when

x \to 7 +

. Therefore

∣ x - 7 ∣ = x - 7

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

Simplify

= x \to 7 + lim (1)

x \to a lim c = c

= 1

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