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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{9}{5}

+1

Dezimale

1.8

Schritte zur Lösung

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

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

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

Wende das L'Hopital Theorem an

= \frac{1}{5} \cdot x \to 0 lim (\frac{3 sin ( 6 x )}{2 x})

Wende das L'Hopital Theorem an

= \frac{1}{5} \cdot x \to 0 lim (\frac{18 cos ( 6 x )}{2})

Setze den Wert

x = 0

ein

= \frac{1}{5} \cdot \frac{18 cos ( 6 \cdot 0 )}{2}

Vereinfache

\frac{1}{5} \cdot \frac{18 cos ( 6 \cdot 0 )}{2} : \frac{9}{5}

= \frac{9}{5}

Graph

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