limit as x approaches 0 of (1-cos(3x))/(1-cos(7x))

Lösung

x \to 0 lim (\frac{1 - cos ( 3 x )}{1 - cos ( 7 x )})

\frac{9}{49}

Dezimale

0.18367 \dots

Schritte zur Lösung

x \to 0 lim (\frac{1 - cos ( 3 x )}{1 - cos ( 7 x )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{3 sin ( 3 x )}{7 sin ( 7 x )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{9 cos ( 3 x )}{49 cos ( 7 x )})

Setze den Wert

x = 0

ein

= \frac{9 cos ( 3 \cdot 0 )}{49 cos ( 7 \cdot 0 )}

Vereinfache

\frac{9 cos ( 3 \cdot 0 )}{49 cos ( 7 \cdot 0 )} : \frac{9}{49}

= \frac{9}{49}

x \to 3 + lim (x^{2} - 9)

(x, y) \to (0, 2) lim (x^{3} y)

\frac{d}{d x} (40 x)

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

\frac{d}{d x} (y^{2}) = 16 x