limit as x approaches infinity of (8\sqrt[x]{x^4})/9

Lösung

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

\frac{8}{9}

Dezimale

0.88888 \dots

Schritte zur Lösung

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

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

= \frac{8}{9} \cdot x \to \infty lim (x x^{4})

Wende Radikal Regel an:

n a^{m} = a^{\frac{m}{n}},

angenommen

a \geq 0

= \frac{8}{9} \cdot x \to \infty lim (x^{\frac{4}{x}})

Wende Exponentenregel an

= \frac{8}{9} \cdot x \to \infty lim (e^{\frac{4}{x} l n (x)})

Wende die Kettenregel für Grenzen an:

1

= \frac{8}{9} \cdot 1

Vereinfache

= \frac{8}{9}

x \to 3 - lim (\frac{9 - 2 x}{3})

\int e^{5 x} sin (6 x) d x

in v erse l a pl a ce \frac{s - 1}{s + 1}

\frac{\partial}{\partial y} (x^{2} - x y + 4 y^{2})

x \to 2 lim (2 x - 7)