What is the limit as x approaches infinity of \sqrt[7]{x} ?

The limit as x approaches infinity of \sqrt[7]{x} is infinity

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limit as x approaches infinity of \sqrt[7]{x}

\infty

Solution steps

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

Apply the common limit:

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

Apply Infinity Property:

\infty^{c} = \infty

= \infty

What is the limit as x approaches infinity of \sqrt[7]{x} ?
The limit as x approaches infinity of \sqrt[7]{x} is infinity