What is the limit as x approaches 6+of (x-6)/(|x-6|) ?

The limit as x approaches 6+of (x-6)/(|x-6|) is 1

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limit as x approaches 6+of (x-6)/(|x-6|)

x \to 6 + lim (\frac{x - 6}{∣ x - 6 ∣})

1

Solution steps

x \to 6 + lim (\frac{x - 6}{∣ x - 6 ∣})

x - 6

is positive when

x \to 6 +

. Therefore

∣ x - 6 ∣ = x - 6

= x \to 6 + lim (\frac{x - 6}{x - 6})

Simplify

= x \to 6 + lim (1)

x \to a lim c = c

= 1

x \to - 2 lim (x^{2} + x - 3)

z \to 8 lim (\frac{2 z ^{2} - 17 z + 8}{8 - z})

x \to 5 lim (\frac{x + 3}{x - 5})

x \to 0 lim (1 - cos (x^{2}))

x \to 0 lim (\frac{x}{( 1 - x ) ^{2}})

What is the limit as x approaches 6+of (x-6)/(|x-6|) ?
The limit as x approaches 6+of (x-6)/(|x-6|) is 1