limit as x approaches 0 of (1-cos(8x))/(1-cos(3x))

Lösung

x \to 0 lim (\frac{1 - cos ( 8 x )}{1 - cos ( 3 x )})

\frac{64}{9}

Dezimale

7.11111 \dots

Schritte zur Lösung

x \to 0 lim (\frac{1 - cos ( 8 x )}{1 - cos ( 3 x )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{8 sin ( 8 x )}{3 sin ( 3 x )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{64 cos ( 8 x )}{9 cos ( 3 x )})

Setze den Wert

x = 0

ein

= \frac{64 cos ( 8 \cdot 0 )}{9 cos ( 3 \cdot 0 )}

Vereinfache

\frac{64 cos ( 8 \cdot 0 )}{9 cos ( 3 \cdot 0 )} : \frac{64}{9}

= \frac{64}{9}

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

x \to 0 lim (e^{c o s (x)})

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

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

x \to 1 lim (x^{3} - 2 x)