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Beliebt Rechnen >

limit as x approaches infinity of (ln(x^5))/(13x)

Lösung

x \to \infty lim (\frac{ln ( x ^{5} )}{13 x})

Lösung

0

Schritte zur Lösung

x \to \infty lim (\frac{ln ( x ^{5} )}{13 x})

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

= \frac{1}{13} \cdot x \to \infty lim (\frac{ln ( x ^{5} )}{x})

ln (x^{5}) = 5 ln (x)

= \frac{1}{13} \cdot x \to \infty lim (\frac{5 ln ( x )}{x})

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

= \frac{1}{13} \cdot 5 \cdot x \to \infty lim (\frac{ln ( x )}{x})

Wende das L'Hopital Theorem an

= \frac{1}{13} \cdot 5 \cdot x \to \infty lim (\frac{\frac{1}{x}}{1})

Vereinfache

= \frac{1}{13} \cdot 5 \cdot x \to \infty lim (\frac{1}{x})

Wende die Unendlichkeitseigenschaft an:

x \to \infty lim (\frac{c}{x ^{a}}) = 0

= \frac{1}{13} \cdot 5 \cdot 0

Vereinfache

\frac{1}{13} \cdot 5 \cdot 0 : 0

= 0

Graph

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