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

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

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

x \to 0 - lim (\frac{x + ∣ x ∣}{x})

0

Solution steps

x \to 0 - lim (\frac{x + ∣ x ∣}{x})

x

is negative when

x \to 0 -

. Therefore

∣ x ∣ = - x

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

Simplify

= x \to 0 - lim (0)

x \to a lim c = c

= 0

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