limit as x approaches 0 of (sin^2(3x))/(sin^2(5x))

Lösung

x \to 0 lim (\frac{sin ^{2} ( 3 x )}{sin ^{2} ( 5 x )})

\frac{9}{25}

Dezimale

0.36

Schritte zur Lösung

x \to 0 lim (\frac{sin ^{2} ( 3 x )}{sin ^{2} ( 5 x )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{3 sin ( 6 x )}{5 sin ( 10 x )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{18 cos ( 6 x )}{50 cos ( 10 x )})

Setze den Wert

x = 0

ein

= \frac{18 cos ( 6 \cdot 0 )}{50 cos ( 10 \cdot 0 )}

Vereinfache

\frac{18 cos ( 6 \cdot 0 )}{50 cos ( 10 \cdot 0 )} : \frac{9}{25}

= \frac{9}{25}

x \to 0 + lim (x \cdot sin (ln (x)))

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

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

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

x \to 3 lim (x^{2} - 6 x + 9)