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

\frac{d}{d x} (arcsin (1 - x^{2}))

y = 2, y = sin (x), x = 0, x = π

\frac{5}{( s ) ( s ^{2} + s + 2 )}

x = 1 \sum \infty \frac{( ( 2 x ) ^{x} )}{x ^{2 x}}

\int \frac{2 x}{π} d x

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