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

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

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

x \to 0 - lim (\frac{ln ∣ x ∣}{x})

\infty

Solution steps

x \to 0 - lim (\frac{ln ∣ x ∣}{x})

x

is negative when

x \to 0 -

. Therefore

∣ x ∣ = - x

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

\frac{ln ( - x )}{x} = ln (- x) \frac{1}{x}

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to 0 - lim (ln (- x)) \cdot x \to 0 - lim (\frac{1}{x})

x \to 0 - lim (ln (- x)) = - \infty

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

= (- \infty) (- \infty)

Apply Infinity Property:

(- \infty) (- \infty) = \infty

= \infty

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

x \to 2 lim (x^{2} + 6 x + 2)

t \to 0 + lim (ln (t))

x \to 3 lim (\frac{4 x - 4}{x - 3})

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

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