What is the limit as x approaches 0 of (1-x^2)^{1/(x^2)} ?

The limit as x approaches 0 of (1-x^2)^{1/(x^2)} is 1/e

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limit as x approaches 0 of (1-x^2)^{1/(x^2)}

x \to 0 lim ((1 - x^{2})^{\frac{1}{x ^{2}}})

\frac{1}{e}

Decimal Notation

0.36787 \dots

Solution steps

x \to 0 lim ((1 - x^{2})^{\frac{1}{x ^{2}}})

Apply exponent rules

= x \to 0 lim (e^{\frac{1}{x ^{2}} l n (1 - x^{2})})

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

x \to \infty lim (\frac{4 x ^{2} - 5 x}{1 - 3 x ^{2}})

x \to \infty lim (\frac{ln ( 3 x )}{x})

x \to \infty lim ((\frac{x + 7}{x + 3})^{2 x})

x \to 0 lim (sin^{s i n (x)} (x))

x \to 0 + lim (\frac{1}{1 + 2 ^{\frac{1}{x}}})

What is the limit as x approaches 0 of (1-x^2)^{1/(x^2)} ?
The limit as x approaches 0 of (1-x^2)^{1/(x^2)} is 1/e