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

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

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

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

\frac{1}{e}

Decimal Notation

0.60653 \dots

Solution steps

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

Apply exponent rules

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

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

f (x) = x^{- 4}

\frac{s ^{2} + 1}{s ^{2} + 2 s + 2}

\int \frac{( e ^{x} )}{x} d x

f (x) 2 x^{2} + 8 x, x = 1

x \to 0 lim ((tan (6 x))^{x})

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