What is the limit as x approaches infinity of 1/(e^{-x)x^5} ?

The limit as x approaches infinity of 1/(e^{-x)x^5} is infinity

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limit as x approaches infinity of 1/(e^{-x)x^5}

x \to \infty lim (\frac{1}{e ^{- x} x ^{5}})

\infty

Solution steps

x \to \infty lim (\frac{1}{e ^{- x} x ^{5}})

For

x

approaching

\infty

e^{- x} x^{5}

is approaching 0 from the right

.

Therefore

x \to \infty lim (\frac{1}{e ^{- x} x ^{5}}) = \infty

= \infty

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What is the limit as x approaches infinity of 1/(e^{-x)x^5} ?
The limit as x approaches infinity of 1/(e^{-x)x^5} is infinity