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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{a ^{2}}{2}

Schritte zur Lösung

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

Wende das L'Hopital Theorem an

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

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{a ^{2} cos ( a x )}{2})

Setze den Wert

x = 0

ein

= \frac{a ^{2} cos ( a \cdot 0 )}{2}

a^{2} cos (a \cdot 0) = a^{2}

= \frac{a ^{2}}{2}

Graph

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