What is the limit as x approaches 0 of (|x|)/(4x) ?

The limit as x approaches 0 of (|x|)/(4x) is diverges

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limit as x approaches 0 of (|x|)/(4x)

x \to 0 lim (\frac{∣ x ∣}{4 x})

diverges

Solution steps

x \to 0 lim (\frac{∣ x ∣}{4 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{∣ x ∣}{4 x}) = \frac{1}{4}

x \to 0 - lim (\frac{∣ x ∣}{4 x}) = - \frac{1}{4}

= diverges

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 36 y = 0

\int_{0}^{42} 2 - x^{\frac{2}{5}} d x

\int tan (\frac{t}{2}) d t

\int_{0}^{1} (x + 7) (x - 8) d x

x \to - 4 lim (- x^{2} + 2 x - 8)

What is the limit as x approaches 0 of (|x|)/(4x) ?
The limit as x approaches 0 of (|x|)/(4x) is diverges