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

x \to 1 lim (5 x \cdot (1 + x))

x \to - \infty lim (e - e^{x})

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

x \to 2 lim (e^{- x})

x \to \frac{π}{2} - lim (1 - sin (x))

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