What is the limit as x approaches 0-of (1-e^x)^{2x} ?

The limit as x approaches 0-of (1-e^x)^{2x} is 1

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limit as x approaches 0-of (1-e^x)^{2x}

x \to 0 - lim ((1 - e^{x})^{2 x})

1

Solution steps

x \to 0 - lim ((1 - e^{x})^{2 x})

Apply exponent rules

= x \to 0 - lim (e^{2 x l n (1 - e^{x})})

Apply the Limit Chain Rule:

1

= 1

What is the limit as x approaches 0-of (1-e^x)^{2x} ?
The limit as x approaches 0-of (1-e^x)^{2x} is 1