limit as x approaches 0 of (5x-tan(5x))/(x^3)

Lösung

x \to 0 lim (\frac{5 x - tan ( 5 x )}{x ^{3}})

- \frac{125}{3}

Dezimale

- 41.66666 \dots

Schritte zur Lösung

x \to 0 lim (\frac{5 x - tan ( 5 x )}{x ^{3}})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{- 5 tan ^{2} ( 5 x )}{3 x ^{2}})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{- 50 sec ^{2} ( 5 x ) tan ( 5 x )}{6 x})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{- 50 ( 10 sec ^{2} ( 5 x ) tan ^{2} ( 5 x ) + 5 sec ^{4} ( 5 x ) )}{6})

Setze den Wert

x = 0

ein

= \frac{- 50 ( 10 sec ^{2} ( 5 \cdot 0 ) tan ^{2} ( 5 \cdot 0 ) + 5 sec ^{4} ( 5 \cdot 0 ) )}{6}

Vereinfache

\frac{- 50 ( 10 sec ^{2} ( 5 \cdot 0 ) tan ^{2} ( 5 \cdot 0 ) + 5 sec ^{4} ( 5 \cdot 0 ) )}{6} : - \frac{125}{3}

= - \frac{125}{3}

x \to - 7 lim (\frac{x ^{2} + 7 x}{x ^{2} - 2 x - 63})

x \to 0 lim (csc (x) sin (sin (x)))

t \to \infty lim (\frac{ln ( 3 t )}{t ^{2}})

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

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