What is the limit as x approaches 0+of (x^2)^x ?

The limit as x approaches 0+of (x^2)^x is 1

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limit as x approaches 0+of (x^2)^x

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

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

x \to 0 lim (arctan (x) - x)

x \to \infty lim (\frac{x ^{2} ln ( x )}{x ^{2.01}})

x \to 2 lim (\frac{3 x + 2}{x - 1})

x \to 0 lim (x csc (6 x))

x \to 0 lim (sin (x) x)

What is the limit as x approaches 0+of (x^2)^x ?
The limit as x approaches 0+of (x^2)^x is 1