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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

x \to 3 lim (- 9)

\frac{d}{d x} (\frac{u}{v})

f (x) = \frac{8}{x ^{2}}

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