limit as x approaches pi/2 of (sin^2(x))^{tan(x)}

Lösung

x \to \frac{π}{2} lim ((sin^{2} (x))^{t a n (x)})

1

Schritte zur Lösung

x \to \frac{π}{2} lim ((sin^{2} (x))^{t a n (x)})

Wende Exponentenregel an

= x \to \frac{π}{2} lim (e^{t a n (x) l n (s i n^{2} (x))})

Wende die Kettenregel für Grenzen an:

1

= 1

x \to - 1 lim (7)

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

x \to - 2 lim (3 x - 4 x^{2})

x \to 0 lim ((x^{2})^{x^{2}})

x \to 6 - lim (\frac{2 x}{x ^{2} - 36})