What is the limit as x approaches infinity of x^{-6} ?

The limit as x approaches infinity of x^{-6} is 0

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limit as x approaches infinity of x^{-6}

x \to \infty lim (x^{- 6})

0

Solution steps

x \to \infty lim (x^{- 6})

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))^{- 6}

Apply the common limit:

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

= \infty^{- 6}

Apply Infinity Property:

\infty^{- c} = 0

= 0

\int - x \cdot e^{3 x} d x

\int x^{2} - y^{2} d y

\int \frac{4 x ^{3} - 6 x ^{4}}{2 x ^{6}} d x

y^{^{'}} = 2 y - x^{2}

(\frac{x ^{2} + x + 4}{x + 1})^{^{'}}

What is the limit as x approaches infinity of x^{-6} ?
The limit as x approaches infinity of x^{-6} is 0