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

Lösung

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

\frac{1}{e}

Dezimale

0.60653 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Wende die Kettenregel für Grenzen an:

\frac{1}{e}

= \frac{1}{e}

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})

x \to \infty lim (- 2 x + 5)