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Beliebt Rechnen >

limit as x approaches 0 of (sin(5x))/(sin(1/3 x))

Lösung

x \to 0 lim (\frac{sin ( 5 x )}{sin ( \frac{1}{3} x )})

Lösung

15

Schritte zur Lösung

x \to 0 lim (\frac{sin ( 5 x )}{sin ( \frac{1}{3} x )})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{cos ( 5 x ) \cdot 5}{cos ( \frac{x}{3} ) \frac{1}{3}})

Setze den Wert

x = 0

ein

= \frac{cos ( 5 \cdot 0 ) \cdot 5}{cos ( \frac{0}{3} ) \frac{1}{3}}

Vereinfache

\frac{cos ( 5 \cdot 0 ) \cdot 5}{cos ( \frac{0}{3} ) \frac{1}{3}} : 15

= 15

Graph

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