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

The limit as x approaches 0+of e^{xln(x)} is 1

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

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

1

Solution steps

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

Simplify

e^{x l n (x)} : x^{x}

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

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

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What is the limit as x approaches 0+of e^{xln(x)} ?
The limit as x approaches 0+of e^{xln(x)} is 1