limit as x approaches 0 of (sin(x))/(sin(2x))

Lösung

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

\frac{1}{2}

Dezimale

0.5

Schritte zur Lösung

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

Wende das L'Hopital Theorem an

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

Setze den Wert

x = 0

ein

= \frac{cos ( 0 )}{cos ( 2 \cdot 0 ) \cdot 2}

Vereinfache

\frac{cos ( 0 )}{cos ( 2 \cdot 0 ) \cdot 2} : \frac{1}{2}

= \frac{1}{2}

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