limit as x approaches 0 of (-sin(x))/x

Lösung

x \to 0 lim (\frac{- sin ( x )}{x})

- 1

Schritte zur Lösung

x \to 0 lim (\frac{- sin ( x )}{x})

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

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

Wende das L'Hopital Theorem an

= - x \to 0 lim (\frac{cos ( x )}{1})

Setze den Wert

x = 0

ein

= - \frac{cos ( 0 )}{1}

Vereinfache

- \frac{cos ( 0 )}{1} : - 1

= - 1