What is the limit as x approaches 0+of x^{x^{1/2}} ?

The limit as x approaches 0+of x^{x^{1/2}} is 1

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limit as x approaches 0+of x^{x^{1/2}}

x \to 0 + lim (x^{x^{\frac{1}{2}}})

1

Solution steps

x \to 0 + lim (x^{x^{\frac{1}{2}}})

Apply exponent rules

= x \to 0 + lim (e^{x^{\frac{1}{2}} l n (x)})

Apply the Limit Chain Rule:

1

= 1

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What is the limit as x approaches 0+of x^{x^{1/2}} ?
The limit as x approaches 0+of x^{x^{1/2}} is 1