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Beliebt Rechnen >

limit as x approaches 0 of (1-cos^2(3x))/(x^2)

Lösung

x \to 0 lim (\frac{1 - cos ^{2} ( 3 x )}{x ^{2}})

Lösung

9

Schritte zur Lösung

x \to 0 lim (\frac{1 - cos ^{2} ( 3 x )}{x ^{2}})

Wende das L'Hopital Theorem an

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

Wende das L'Hopital Theorem an

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

Setze den Wert

x = 0

ein

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

Vereinfache

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

= 9

Graph

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