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

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

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

x \to 0 + lim (\frac{x + ∣ x ∣}{x})

2

Solution steps

x \to 0 + lim (\frac{x + ∣ x ∣}{x})

x

is positive when

x \to 0 +

. Therefore

∣ x ∣ = x

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

\frac{x + x}{x} = 2

= x \to 0 + lim (2)

x \to a lim c = c

= 2

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