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Limit of the function x^(-1/3)

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       1  
 lim -----
x->oo3 ___
     \/ x

\lim_{x \to \infty} \frac{1}{\sqrt[3]{x}}

Limit(x^(-1/3), x, oo, dir='-')

Lopital's rule

There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type

The graph

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Rapid solution [src]

0

Expand and simplify

Other limits x→0, -oo, +oo, 1

\lim_{x \to \infty} \frac{1}{\sqrt[3]{x}} = 0

\lim_{x \to 0^-} \frac{1}{\sqrt[3]{x}} = - \infty \left(-1\right)^{\frac{2}{3}}

\lim_{x \to 0^+} \frac{1}{\sqrt[3]{x}} = \infty

\lim_{x \to 1^-} \frac{1}{\sqrt[3]{x}} = 1

\lim_{x \to 1^+} \frac{1}{\sqrt[3]{x}} = 1

\lim_{x \to -\infty} \frac{1}{\sqrt[3]{x}} = 0

The graph