limit as x approaches-infinity of x^7e^x

Lösung

x \to - \infty lim (x^{7} e^{x})

0

Schritte zur Lösung

x \to - \infty lim (x^{7} e^{x})

Umformung für L'Hopital

= x \to - \infty lim (\frac{x ^{7}}{\frac{1}{e ^{x}}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{7 x ^{6}}{- e ^{- x}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{42 x ^{5}}{e ^{- x}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{210 x ^{4}}{- e ^{- x}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{840 x ^{3}}{e ^{- x}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{2520 x ^{2}}{- e ^{- x}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{5040 x}{e ^{- x}})

Wende das L'Hopital Theorem an

= x \to - \infty lim (\frac{5040}{- e ^{- x}})

Vereinfache

\frac{5040}{- e ^{- x}} : - 5040 e^{x}

= x \to - \infty lim (- 5040 e^{x})

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

= - 5040 \cdot x \to - \infty lim (e^{x})

Wende die allgemeine Grenze an:

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

= - 5040 \cdot 0

Vereinfache

= 0

x \to \infty lim (e^{x} + 2)

x \to 0 - lim (sin (x) ln (x))

x \to - 3 lim (x^{2} - 4)

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

x \to \frac{π}{2} lim (\frac{cos ( x )}{x})