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Beliebt Rechnen >

limit as x approaches 0 of (2sin(3x))/(5x)

Lösung

x \to 0 lim (\frac{2 sin ( 3 x )}{5 x})

Lösung

\frac{6}{5}

+1

Dezimale

1.2

Schritte zur Lösung

x \to 0 lim (\frac{2 sin ( 3 x )}{5 x})

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

= \frac{2}{5} \cdot x \to 0 lim (\frac{sin ( 3 x )}{x})

Wende das L'Hopital Theorem an

= \frac{2}{5} \cdot x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{1})

Setze den Wert

x = 0

ein

= \frac{2}{5} \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1}

Vereinfache

\frac{2}{5} \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1} : \frac{6}{5}

= \frac{6}{5}

Graph

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