limit as x approaches pi/4 of 7tan^{tan(2x)}(x)

Lösung

x \to \frac{π}{4} lim (7 tan^{t a n (2 x)} (x))

\frac{7}{e}

Dezimale

2.57515 \dots

Schritte zur Lösung

x \to \frac{π}{4} lim (7 tan^{t a n (2 x)} (x))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 7 \cdot x \to \frac{π}{4} lim (tan^{t a n (2 x)} (x))

Wende Exponentenregel an

= 7 \cdot x \to \frac{π}{4} lim (e^{t a n (2 x) l n (t a n (x))})

Wende die Kettenregel für Grenzen an:

\frac{1}{e}

= 7 \cdot \frac{1}{e}

Vereinfache

7 \cdot \frac{1}{e} : \frac{7}{e}

= \frac{7}{e}