What is the limit as x approaches-infinity of x^{-5} ?

The limit as x approaches-infinity of x^{-5} is 0

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limit as x approaches-infinity of x^{-5}

x \to - \infty lim (x^{- 5})

0

Solution steps

x \to - \infty lim (x^{- 5})

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))^{- 5}

Apply the common limit:

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

= (- \infty)^{- 5}

Simplify

(- \infty)^{- 5} : 0

= 0

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What is the limit as x approaches-infinity of x^{-5} ?
The limit as x approaches-infinity of x^{-5} is 0