limit as x approaches 0 of (ln(cos(x)))/(ln(cos(2x)))

Lösung

x \to 0 lim (\frac{ln ( cos ( x ) )}{ln ( cos ( 2 x ) )})

\frac{1}{4}

Dezimale

0.25

Schritte zur Lösung

x \to 0 lim (\frac{ln ( cos ( x ) )}{ln ( cos ( 2 x ) )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{- tan ( x )}{- 2 tan ( 2 x )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{- sec ^{2} ( x )}{- 4 sec ^{2} ( 2 x )})

Setze den Wert

x = 0

ein

= \frac{- sec ^{2} ( 0 )}{- 4 sec ^{2} ( 2 \cdot 0 )}

Vereinfache

\frac{- sec ^{2} ( 0 )}{- 4 sec ^{2} ( 2 \cdot 0 )} : \frac{1}{4}

= \frac{1}{4}

\int (x - 3)^{3} d x

(x^{2} + 1) \frac{d y}{d x} + 5 x (y - 1) = 0, y (0) = 4

\int \frac{sin ( 2 x )}{1 + cos ^{2} ( x )} d x

\frac{d y}{d x} = \frac{sec ( y )}{( x + 5 ) ^{2}}

\int \frac{1}{x ^{2} x ^{2} - 121} d x