limit as x approaches 0 of (tan(x)((1-cos(x))))/(xxx)

Lösung

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

\frac{1}{2}

Dezimale

0.5

Schritte zur Lösung

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

Vereinfache

\frac{tan ( x ) ( 1 - cos ( x ) )}{xxx} : \frac{- sin ( x ) + tan ( x )}{x ^{3}}

= x \to 0 lim (\frac{- sin ( x ) + tan ( x )}{x ^{3}})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{- cos ( x ) + sec ^{2} ( x )}{3 x ^{2}})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{sin ( x ) + 2 sec ^{2} ( x ) tan ( x )}{6 x})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{cos ( x ) - 4 sec ^{2} ( x ) + 6 sec ^{4} ( x )}{6})

Setze den Wert

x = 0

ein

= \frac{cos ( 0 ) - 4 sec ^{2} ( 0 ) + 6 sec ^{4} ( 0 )}{6}

Vereinfache

\frac{cos ( 0 ) - 4 sec ^{2} ( 0 ) + 6 sec ^{4} ( 0 )}{6} : \frac{1}{2}

= \frac{1}{2}

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

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

x \to 0 + lim (\frac{2}{x ^{3}})

θ \to \frac{5 π}{6} lim (cos (θ))

x \to 1 + lim (12 ∣ 2 x - 1 ∣ + a)