limit as x approaches 0 of 3 x/(sin(x))

Lösung

x \to 0 lim (3 \frac{x}{sin ( x )})

3

Schritte zur Lösung

x \to 0 lim (3 \cdot \frac{x}{sin ( x )})

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

= 3 \cdot x \to 0 lim (\frac{x}{sin ( x )})

Wende das L'Hopital Theorem an

= 3 \cdot x \to 0 lim (\frac{1}{cos ( x )})

Setze den Wert

x = 0

ein

= 3 \cdot \frac{1}{cos ( 0 )}

Vereinfache

3 \cdot \frac{1}{cos ( 0 )} : 3

= 3

x \to 0 + lim (x^{\frac{10}{x}})

x \to 0 - lim (6 (cot (x) - \frac{1}{x}))

x \to - 3 lim (\frac{1}{x ^{2}})

x \to 0 lim (π coth (\frac{1}{x}))

x \to 2 + lim (\frac{x ^{2} + 2}{x - 2})