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

Lösung

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

\frac{1}{e}

Dezimale

0.60653 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Wende Exponentenregel an

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

Wende die Kettenregel für Grenzen an:

\frac{1}{e}

= \frac{1}{e}

x \to - \infty lim (- 2^{x} - 7)

x \to 0 lim (\frac{3 x ^{2}}{1 + x sin ( x ) - cos ( x )})

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

x \to \infty lim (\frac{6 x ^{2} - 7 x + 10}{5 x ^{3} + 2 x ^{2} - 4 x + 5})

x \to 0 lim (x^{2} lo g_{e} (x))