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Beliebt Rechnen >

limit as x approaches 0 of (2x^2)/(sin^2(8x))

Lösung

x \to 0 lim (\frac{2 x ^{2}}{sin ^{2} ( 8 x )})

Lösung

\frac{1}{32}

+1

Dezimale

0.03125

Schritte zur Lösung

x \to 0 lim (\frac{2 x ^{2}}{sin ^{2} ( 8 x )})

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

= 2 \cdot x \to 0 lim (\frac{x ^{2}}{sin ^{2} ( 8 x )})

Wende das L'Hopital Theorem an

= 2 \cdot x \to 0 lim (\frac{2 x}{16 sin ( 8 x ) cos ( 8 x )})

Wende das L'Hopital Theorem an

= 2 \cdot x \to 0 lim (\frac{2}{128 cos ( 16 x )})

Setze den Wert

x = 0

ein

= 2 \cdot \frac{2}{128 cos ( 16 \cdot 0 )}

Vereinfache

2 \cdot \frac{2}{128 cos ( 16 \cdot 0 )} : \frac{1}{32}

= \frac{1}{32}

Graph

Beliebte Beispiele

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