What is the limit as x approaches infinity of x^{-e} ?

The limit as x approaches infinity of x^{-e} is 0

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limit as x approaches infinity of x^{-e}

x \to \infty lim (x^{- e})

0

Solution steps

x \to \infty lim (x^{- e})

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

With the exception of indeterminate form

= (x \to \infty lim (x))^{- e}

Apply the common limit:

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

= \infty^{- e}

Apply Infinity Property:

\infty^{- c} = 0

= 0

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What is the limit as x approaches infinity of x^{-e} ?
The limit as x approaches infinity of x^{-e} is 0