What is the limit as x approaches 1 of x^{1/(x^2-1)} ?

The limit as x approaches 1 of x^{1/(x^2-1)} is sqrt(e)

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limit as x approaches 1 of x^{1/(x^2-1)}

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

e

Decimal Notation

1.64872 \dots

Solution steps

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

Apply exponent rules

= x \to 1 lim (e^{\frac{1}{x ^{2} - 1} l n (x)})

Apply the Limit Chain Rule:

e

= e

\frac{1}{3 s ^{2}} - \frac{5}{2 s}

y = 3 x, y = x

\frac{d}{d x} (ln (x^{4} 8 - 6 x))

g (x) = \frac{1 - 3 x}{5 + x}

tan^{2} (4 x)

What is the limit as x approaches 1 of x^{1/(x^2-1)} ?
The limit as x approaches 1 of x^{1/(x^2-1)} is sqrt(e)