What is the limit as x approaches 0+of (x)^{1/x} ?

The limit as x approaches 0+of (x)^{1/x} is 0

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limit as x approaches 0+of (x)^{1/x}

x \to 0 + lim ((x)^{\frac{1}{x}})

0

Solution steps

x \to 0 + lim (x^{\frac{1}{x}})

Apply exponent rules

= x \to 0 + lim (e^{\frac{1}{x} l n (x)})

Apply the Limit Chain Rule:

0

= 0

x \to 3 lim (\frac{5 - x}{x - 2})

x \to 0 lim (x arctan (x))

x \to 3 lim ((3 x) (4 x))

x \to \frac{π}{2} lim (arctan (x))

h \to 0 lim (3 x^{2} + 3 x h + h^{2})

What is the limit as x approaches 0+of (x)^{1/x} ?
The limit as x approaches 0+of (x)^{1/x} is 0