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

The limit as x approaches 0+of x/(x+|x|) is 1/2

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

x \to 0 + lim (\frac{x}{x + ∣ x ∣})

\frac{1}{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} = \frac{1}{2}

= x \to 0 + lim (\frac{1}{2})

x \to a lim c = c

= \frac{1}{2}

\frac{\partial}{\partial x} (z^{3} - 3 x yz)

\frac{\partial}{\partial x} (e^{9 x e^{y}})

\frac{\partial}{\partial x} (sin^{2} (3 x))

\int csc^{9} (x) d x

x \to 0 lim (x^{2} - 3 x + 3)

What is the limit as x approaches 0+of x/(x+|x|) ?
The limit as x approaches 0+of x/(x+|x|) is 1/2