What is the limit as x approaches infinity of \sqrt[x]{2}-1 ?

The limit as x approaches infinity of \sqrt[x]{2}-1 is 0

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limit as x approaches infinity of \sqrt[x]{2}-1

0

Solution steps

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

x \to \infty lim (1) = 1

= 1 - 1

Simplify

= 0

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What is the limit as x approaches infinity of \sqrt[x]{2}-1 ?
The limit as x approaches infinity of \sqrt[x]{2}-1 is 0