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

\int cos^{9} (x) tan^{3} (x) d x

25 y^{^{''}} - 40 y^{^{'}} + 16 y = 0, y (0) = 2, y^{^{'}} (0) = 3

\int \frac{24 x ^{2}}{36 - x ^{2}} d x

x \to 1 lim (6 x + 4)

\frac{( e ^{\frac{s}{2}} )}{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