limit as x approaches pi-of (x-pi)csc(x)

Lösung

x \to π - lim ((x - π) csc (x))

- 1

Schritte zur Lösung

x \to π - lim ((x - π) csc (x))

Umformung für L'Hopital

= x \to π - lim (\frac{x - π}{\frac{1}{c s c ( x )}})

Wende das L'Hopital Theorem an

= x \to π - lim (\frac{1}{cos ( x )})

Setze den Wert

x = π

ein

= \frac{1}{cos ( π )}

Vereinfache

\frac{1}{cos ( π )} : - 1

= - 1

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