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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

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