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

Lösung

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

\frac{2}{3}

Dezimale

0.66666 \dots

Schritte zur Lösung

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{3} \cdot x \to 0 lim (\frac{sin ( 2 x )}{x})

Wende das L'Hopital Theorem an

= \frac{1}{3} \cdot x \to 0 lim (\frac{cos ( 2 x ) \cdot 2}{1})

Setze den Wert

x = 0

ein

= \frac{1}{3} \cdot \frac{cos ( 2 \cdot 0 ) \cdot 2}{1}

Vereinfache

\frac{1}{3} \cdot \frac{cos ( 2 \cdot 0 ) \cdot 2}{1} : \frac{2}{3}

= \frac{2}{3}

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