What is the limit as x approaches infinity of 1/(xln(x)(ln(ln(x)))^{-1)} ?

The limit as x approaches infinity of 1/(xln(x)(ln(ln(x)))^{-1)} is 0

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limit as x approaches infinity of 1/(xln(x)(ln(ln(x)))^{-1)}

x \to \infty lim (\frac{1}{x ln ( x ) ( ln ( ln ( x ) ) ) ^{- 1}})

0

Solution steps

x \to \infty lim (\frac{1}{x ln ( x ) ( ln ( ln ( x ) ) ) ^{- 1}})

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 \infty} ( 1 )}{lim _{x \to \infty} ( x ln ( x ) ( ln ( ln ( x ) ) ) ^{- 1} )}

x \to \infty lim (1) = 1

x \to \infty lim (x ln (x) (ln (ln (x)))^{- 1}) = \infty

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

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What is the limit as x approaches infinity of 1/(xln(x)(ln(ln(x)))^{-1)} ?
The limit as x approaches infinity of 1/(xln(x)(ln(ln(x)))^{-1)} is 0