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

The limit as x approaches 0+of x^{ln(x)} is infinity

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limit as x approaches 0+of x^{ln(x)}

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

\infty

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\infty

= \infty

x \to - 2 lim (4)

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

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

x \to 3 lim (\frac{x ^{3} - 9 x}{3 x ^{2} - 6 x - 9})

x \to 1 lim (2 x^{2} + 5 x - 6)

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