limit as θ approaches 0 of (sin(θ))/(2θ)

Lösung

θ \to 0 lim (\frac{sin ( θ )}{2 θ})

\frac{1}{2}

Dezimale

0.5

Schritte zur Lösung

θ \to 0 lim (\frac{sin ( θ )}{2 θ})

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

= \frac{1}{2} \cdot θ \to 0 lim (\frac{sin ( θ )}{θ})

Wende das L'Hopital Theorem an

= \frac{1}{2} \cdot θ \to 0 lim (\frac{cos ( θ )}{1})

Setze den Wert

θ = 0

ein

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

Vereinfache

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

= \frac{1}{2}

x \to 3 lim (\frac{x + 33 - 6}{x - 3})

x \to 4 lim (3 x - 5)

x \to 0 lim (x^{2} \cdot ln (- x))

x \to 2 lim (\frac{4 - 4}{0 \cdot 2 ^{2}})

x \to 0 lim (\frac{1}{2 + e ^{\frac{1}{x}}})