What is the limit as x approaches infinity of (\sqrt[x]{x})/(sqrt(x)) ?

The limit as x approaches infinity of (\sqrt[x]{x})/(sqrt(x)) is 0

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limit as x approaches infinity of (\sqrt[x]{x})/(sqrt(x))

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

0

Solution steps

x \to \infty lim (\frac{x x}{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 \infty} ( x x )}{lim _{x \to \infty} ( x )}

x \to \infty lim (x x) = 1

x \to \infty lim (x) = \infty

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

x \to 0 lim (x ln ∣ 8 x ∣)

x \to 3 - lim (\frac{x + 1}{x ^{2} - 9})

x \to 2 - lim (x^{2} - 4 x + 1)

x \to \frac{π}{4} lim (\frac{1}{2} cos (x))

x \to \infty lim ((1 - (2 x)^{- 1})^{x})

What is the limit as x approaches infinity of (\sqrt[x]{x})/(sqrt(x)) ?
The limit as x approaches infinity of (\sqrt[x]{x})/(sqrt(x)) is 0