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

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

x \to 0 - lim (\frac{3 x - 1}{2 x})

\int \frac{x}{a x ^{2} + b} d x

\int cot (23 x) d x

x \to 3 lim (x^{2} - x + 1)

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