limit as x approaches 0 of (ln(cos(3x)))/(ln(cos(5x)))

Lösung

x \to 0 lim (\frac{ln ( cos ( 3 x ) )}{ln ( cos ( 5 x ) )})

\frac{9}{25}

Dezimale

0.36

Schritte zur Lösung

x \to 0 lim (\frac{ln ( cos ( 3 x ) )}{ln ( cos ( 5 x ) )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{- 3 tan ( 3 x )}{- 5 tan ( 5 x )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{- 9 sec ^{2} ( 3 x )}{- 25 sec ^{2} ( 5 x )})

Setze den Wert

x = 0

ein

= \frac{- 9 sec ^{2} ( 3 \cdot 0 )}{- 25 sec ^{2} ( 5 \cdot 0 )}

Vereinfache

\frac{- 9 sec ^{2} ( 3 \cdot 0 )}{- 25 sec ^{2} ( 5 \cdot 0 )} : \frac{9}{25}

= \frac{9}{25}

h \to 0 lim (\frac{( 2 + h ) ^{5} - 32}{h})

x \to - \infty lim (x^{2 n})

x \to \infty lim (\frac{2}{+ x})

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

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