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Beliebt Rechnen >

limit as x approaches 0+of x^2csc^2(x)

Lösung

x \to 0 + lim (x^{2} csc^{2} (x))

Lösung

1

Schritte zur Lösung

x \to 0 + lim (x^{2} csc^{2} (x))

Umformung für L'Hopital

= x \to 0 + lim (\frac{x ^{2}}{\frac{1}{c s c ^{2} ( x )}})

Wende das L'Hopital Theorem an

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

Wende das L'Hopital Theorem an

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

Setze den Wert

x = 0

ein

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

Vereinfache

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

= 1

Graph

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