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Beliebt Rechnen >

limit as x approaches infinity of (3^{x+4})/(8^x)

Lösung

x \to \infty lim (\frac{3 ^{x + 4}}{8 ^{x}})

Lösung

0

Schritte zur Lösung

x \to \infty lim (\frac{3 ^{x + 4}}{8 ^{x}})

Vereinfache

3^{x + 4} : 3^{x} \cdot 3^{4}

= x \to \infty lim (\frac{3 ^{x} \cdot 3 ^{4}}{8 ^{x}})

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

= 3^{4} \cdot x \to \infty lim (\frac{3 ^{x}}{8 ^{x}})

Vereinfache

= 81 \cdot x \to \infty lim (\frac{3 ^{x}}{8 ^{x}})

Wende Exponentenregel an:

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

= 81 \cdot x \to \infty lim ((\frac{3}{8})^{x})

Wende die allgemeine Grenze an:

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

= 81 \cdot 0

Vereinfache

= 0

Graph

Beliebte Beispiele

derivative of (x^4+y^4/(xy))

\frac{d}{d x} (\frac{x ^{4} + y ^{4}}{x y})

tangent f(x)=-3x^2-2x,\at x=2

t an g e n t f (x) = - 3 x^{2} - 2 x, at x = 2

sum from n=0 to infinity of (4/10)^n

n = 0 \sum \infty (\frac{4}{10})^{n}

integral from 2 to 3 of 21t^2

\int_{2}^{3} 21 t^{2} d t

derivative of 4x+12y,12x-3y

\frac{d}{d x} (4 x + 12 y, 12 x - 3 y)