What is the limit as x approaches 0+of (|2x|)/x ?

The limit as x approaches 0+of (|2x|)/x is 2

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limit as x approaches 0+of (|2x|)/x

x \to 0 + lim (\frac{∣ 2 x ∣}{x})

2

Solution steps

x \to 0 + lim (\frac{∣ 2 x ∣}{x})

2 x

is positive when

x \to 0 +

. Therefore

∣ 2 x ∣ = 2 x

= x \to 0 + lim (\frac{2 x}{x})

Cancel the common factor:

x

= x \to 0 + lim (2)

x \to a lim c = c

= 2

What is the limit as x approaches 0+of (|2x|)/x ?
The limit as x approaches 0+of (|2x|)/x is 2