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

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

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limit as x approaches 1 of (x)^{1/(x-1)}

x \to 1 lim ((x)^{\frac{1}{x - 1}})

e

Decimal Notation

2.71828 \dots

Solution steps

x \to 1 lim (x^{\frac{1}{x - 1}})

Apply exponent rules

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

Apply the Limit Chain Rule:

e

= e

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