What is the limit as x approaches 2+of (x-2)/(|2-x|) ?

The limit as x approaches 2+of (x-2)/(|2-x|) is 1

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limit as x approaches 2+of (x-2)/(|2-x|)

x \to 2 + lim (\frac{x - 2}{∣ 2 - x ∣})

1

Solution steps

x \to 2 + lim (\frac{x - 2}{∣ 2 - x ∣})

2 - x

is negative when

x \to 2 +

. Therefore

∣ 2 - x ∣ = - 2 + x

= x \to 2 + lim (\frac{x - 2}{- 2 + x})

Simplify

= x \to 2 + lim (1)

x \to a lim c = c

= 1

x \to 1 lim (\frac{3 x + 5}{x + 1})

y \to 1 lim (\frac{y ^{3} - 1}{y - 1})

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

x \to 0 + lim (x^{\frac{1}{4}} \cdot ln (x))

x \to 0 lim (F (x))

What is the limit as x approaches 2+of (x-2)/(|2-x|) ?
The limit as x approaches 2+of (x-2)/(|2-x|) is 1