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

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

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

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

diverges

Solution steps

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

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

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

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

= diverges

x \to 0 lim (\frac{x ^{2} + 4 x}{x})

f (x) = x e^{x} + e^{x}

\frac{- 3 s - 20}{s ^{2} + 256}

\int \frac{2 u}{u ^{2} + 1} d u

166 y^{^{''}} + 135 y^{^{'}} + 1313 y = 36 \cdot 0.7 cos (x)

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