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

The limit as z approaches 0 of (cos(z))^{1/(z^2)} is 1/(sqrt(e))

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limit as z approaches 0 of (cos(z))^{1/(z^2)}

z \to 0 lim ((cos (z))^{\frac{1}{z ^{2}}})

\frac{1}{e}

Decimal Notation

0.60653 \dots

Solution steps

z \to 0 lim ((cos (z))^{\frac{1}{z ^{2}}})

Apply exponent rules

= z \to 0 lim (e^{\frac{1}{z ^{2}} l n (c o s (z))})

Apply the Limit Chain Rule:

\frac{1}{e}

= \frac{1}{e}

x \to \infty lim (\frac{( 2 sin ( 3 x ) )}{5 x})

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

x \to - 3 lim (x^{2} + 5 x + 6)

x \to \infty lim (- x^{0})

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

What is the limit as z approaches 0 of (cos(z))^{1/(z^2)} ?
The limit as z approaches 0 of (cos(z))^{1/(z^2)} is 1/(sqrt(e))