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

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

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

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

\frac{1}{e}

Decimal Notation

0.36787 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

x \to - 2 - lim (\frac{∣ x + 2 ∣}{x + 2})

x \to 1 lim (\frac{ln ( x )}{e ^{x}})

x \to \infty lim (3 x^{2} + x)

x \to - \infty lim (- 3 x^{4})

x \to - 2 + lim (\frac{x}{x + 2})

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