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

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

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limit as x approaches 0+of x^{(e^x-1)}

x \to 0 + lim (x^{(e^{x} - 1)})

1

Solution steps

x \to 0 + lim (x^{e^{x} - 1})

Apply exponent rules

= x \to 0 + lim (e^{(e^{x} - 1) l n (x)})

Apply the Limit Chain Rule:

1

= 1

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