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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

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