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

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

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limit as x approaches infinity of (x^{ln(n)})/(x^{ln(n)+1)}

x \to \infty lim (\frac{x ^{l n (n)}}{x ^{l n (n) + 1}})

0

Solution steps

x \to \infty lim (\frac{x ^{l n (n)}}{x ^{l n (n) + 1}})

Simplify

\frac{x ^{l n (n)}}{x ^{l n (n) + 1}} : \frac{1}{x}

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

Apply Infinity Property:

x \to \infty lim (\frac{c}{x ^{a}}) = 0

= 0

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