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 - 1)^{2} + 2, (- 1, 2)

\frac{\partial}{\partial x} (- \frac{y}{y ^{2} + x ^{2}})

\frac{x}{4 + x ^{2}}

y^{^{'}} + y = x y^{3}

y = (\frac{x ^{2} + 3}{x ^{2} - 3})^{4}

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