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Beliebt Rechnen >

limit as x approaches infinity of (e^{4x})/(5x)

Lösung

x \to \infty lim (\frac{e ^{4 x}}{5 x})

Lösung

\infty

Schritte zur Lösung

x \to \infty lim (\frac{e ^{4 x}}{5 x})

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

= \frac{1}{5} \cdot x \to \infty lim (\frac{e ^{4 x}}{x})

Wende das L'Hopital Theorem an

= \frac{1}{5} \cdot x \to \infty lim (\frac{e ^{4 x} \cdot 4}{1})

Vereinfache

= \frac{1}{5} \cdot x \to \infty lim (4 e^{4 x})

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

= \frac{1}{5} \cdot 4 \cdot x \to \infty lim (e^{4 x})

Wende die Kettenregel für Grenzen an:

\infty

= \frac{1}{5} \cdot 4 \cdot \infty

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

Graph

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