What is the limit as x approaches 9+of (|x-9|)/(x-9) ?

The limit as x approaches 9+of (|x-9|)/(x-9) is 1

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limit as x approaches 9+of (|x-9|)/(x-9)

x \to 9 + lim (\frac{∣ x - 9 ∣}{x - 9})

1

Solution steps

x \to 9 + lim (\frac{∣ x - 9 ∣}{x - 9})

x - 9

is positive when

x \to 9 +

. Therefore

∣ x - 9 ∣ = x - 9

= x \to 9 + lim (\frac{x - 9}{x - 9})

Simplify

= x \to 9 + lim (1)

x \to a lim c = c

= 1

x \to 0 lim (cot (\frac{π}{2} - x))

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What is the limit as x approaches 9+of (|x-9|)/(x-9) ?
The limit as x approaches 9+of (|x-9|)/(x-9) is 1