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Beliebt Rechnen >

limit as x approaches infinity of (4^x)/(5^{x+1)}

Lösung

x \to \infty lim (\frac{4 ^{x}}{5 ^{x + 1}})

Lösung

0

Schritte zur Lösung

x \to \infty lim (\frac{4 ^{x}}{5 ^{x + 1}})

Vereinfache

5^{x + 1} : 5^{x} \cdot 5

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

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{4 ^{x}}{5 ^{x}})

Wende Exponentenregel an:

\frac{a ^{c}}{b ^{c}} = (\frac{a}{b})^{c}

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

Wende die allgemeine Grenze an:

x \to \infty lim (a^{x}) = 0, 0 < a < 1

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

Vereinfache

= 0

Graph

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