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

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

\frac{d}{d x} (\frac{1}{( 1 + x )})

(1 + 2 x) e^{3 x^{2}}

y^{^{''}} - 14 y^{^{'}} + 48 y = 0

\frac{3}{s \cdot ( s + 2 )}

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