limit as x approaches pi/2 of (1+cos(x))^{3sec(x)}

Lösung

x \to \frac{π}{2} lim ((1 + cos (x))^{3 s e c (x)})

e^{3}

Dezimale

20.08553 \dots

Schritte zur Lösung

x \to \frac{π}{2} lim ((1 + cos (x))^{3 s e c (x)})

Wende Exponentenregel an

= x \to \frac{π}{2} lim (e^{3 s e c (x) l n (1 + c o s (x))})

Wende die Kettenregel für Grenzen an:

e^{3}

= e^{3}

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

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

x \to 0 lim (\frac{x + cos ( x )}{x})

x \to 0 + lim ((x + sin (x))^{x})

x \to 0 lim (\frac{1}{x} - \frac{1}{x ^{3} - x})