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

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

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)