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

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

im pl i c i t \frac{d y}{d x}, x y = 7

\int \frac{2 x ^{2}}{x ^{2} - 1} d x

\frac{d y}{d x} = e^{4 x} + 9 y

\int 2 x^{4} e^{x^{5}} d x

t an g e n t f (x) = x^{2} + 6, at x = - 7

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