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

Lösung

θ \to 0 lim (sin (θ) cot (2 θ))

\frac{1}{2}

Dezimale

0.5

Schritte zur Lösung

θ \to 0 lim (sin (θ) cot (2 θ))

Umformung für L'Hopital

= θ \to 0 lim (\frac{sin ( θ )}{\frac{1}{c o t ( 2 θ )}})

Wende das L'Hopital Theorem an

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

Setze den Wert

θ = 0

ein

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

Vereinfache

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

= \frac{1}{2}

x \to 0 + lim (tan (9 x))

x \to 1 lim (\frac{9 x ^{8}}{5 x ^{4}})

x \to \infty lim (\frac{sin ( x )}{x ^{4}})

x \to \infty lim ((\frac{( x + 1 )}{x - 1})^{x - 1})

x \to 2 + lim (\frac{x + 1}{x ^{2} - 5 x + 6})