limit as x approaches-infinity of x^6e^x

Lösung

x \to - \infty lim (x^{6} e^{x})

0

Schritte zur Lösung

x \to - \infty lim (x^{6} e^{x})

Umformung für L'Hopital

= x \to - \infty lim (\frac{x ^{6}}{\frac{1}{e ^{x}}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{6 x ^{5}}{- e ^{- x}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{30 x ^{4}}{e ^{- x}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{120 x ^{3}}{- e ^{- x}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{360 x ^{2}}{e ^{- x}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{720 x}{- e ^{- x}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{720}{e ^{- x}})

Vereinfache

\frac{720}{e ^{- x}} : 720 e^{x}

= x \to - \infty lim (720 e^{x})

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

= 720 \cdot x \to - \infty lim (e^{x})

Wende die allgemeine Grenze an:

x \to - \infty lim (e^{x}) = 0

= 720 \cdot 0

Vereinfache

= 0

\frac{d}{d x} (ln (e^{- x}))

\int \frac{y - 2}{y ( y - 4 ) ( y + 3 )} d y

d er i v a t i v e \frac{( x ^{2} - 4 )}{x}

\frac{d}{d x} ((ln (x + 1)) 2 - e^{x^{2}})

\int \frac{2}{4 + x ^{2}} d x