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^{x^{2}})

1

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

\int_{0}^{\infty} \frac{x}{x ^{2} + 1} d x

\int e^{15 x} (15) d x

x \to 4 lim (\frac{x - 4}{x - 2})

f (x) = cos (x), g (x) = - cos (x) + 2

(- 1.4) (3.12)

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