What is the limit as x approaches infinity of x^{-8} ?

The limit as x approaches infinity of x^{-8} is 0

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limit as x approaches infinity of x^{-8}

x \to \infty lim (x^{- 8})

0

Solution steps

x \to \infty lim (x^{- 8})

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))^{- 8}

Apply the common limit:

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

= \infty^{- 8}

Apply Infinity Property:

\infty^{- c} = 0

= 0

x \to 1 lim (x^{2} - 6)

x \to - 8 + lim (\frac{1}{( x + 8 ) ^{2}})

x \to 0 + lim (2 x + 1)

x \to - 2 + lim (- x)

x \to \infty lim (- 3, + x)

What is the limit as x approaches infinity of x^{-8} ?
The limit as x approaches infinity of x^{-8} is 0