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

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

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

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

1

Solution steps

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

2 - x

is positive when

x \to 2 -

. Therefore

∣ 2 - x ∣ = 2 - x

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

Simplify

= x \to 2 - lim (1)

x \to a lim c = c

= 1

x \to - 2 - lim (x^{2} - 4 x + 6)

x \to - π lim (sin (- \frac{x}{2}))

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

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

q \to 2 lim (\frac{4 q ^{2} - q + 2}{8})

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