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

\frac{d}{d y} (\frac{x}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{3}{2}}})

\int \frac{1}{x x ^{2} - π} d x

\int_{0}^{1} e^{x} - x d x

\int x sin (3 x) d x

y = 2 cos (x), y = 6 - 4 cos (x), 0 \leq x \leq 2 π

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