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

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

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

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

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