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

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

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

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

e

Decimal

2.71828 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

e

= e

x \to \infty lim (\frac{1}{7 x})

x \to 5 lim (sec^{2} (π))

x \to 9 + lim (f (x))

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

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

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