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

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

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

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

0

Solution steps

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

ln (x)

is negative when

x \to 0 +

. Therefore

∣ ln (x) ∣ = - ln (x)

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

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

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

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

x \to 0 + lim (1) = 1

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

= - \frac{1}{- \infty}

Apply Infinity Property:

\frac{c}{- \infty} = 0

= 0

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

x \to 1 lim (5 x \cdot (1 + x))

x \to - \infty lim (e - e^{x})

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

x \to 2 lim (e^{- x})

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