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Beliebt Rechnen >

limit as x approaches infinity of (x^3)/(2^x)

Lösung

x \to \infty lim (\frac{x ^{3}}{2 ^{x}})

Lösung

0

Schritte zur Lösung

x \to \infty lim (\frac{x ^{3}}{2 ^{x}})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{3 x ^{2}}{2 ^{x} ln ( 2 )})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{6 x}{ln ^{2} ( 2 ) \cdot 2 ^{x}})

Wende das L'Hopital Theorem an

= x \to \infty lim (\frac{6}{ln ^{3} ( 2 ) \cdot 2 ^{x}})

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

= \frac{6}{ln ^{3} ( 2 )} \cdot x \to \infty lim (\frac{1}{2 ^{x}})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

mit Einschränkung des unbestimmten Ausdrucks

= \frac{6}{ln ^{3} ( 2 )} \cdot \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( 2 ^{x} )}

x \to \infty lim (1) = 1

x \to \infty lim (2^{x}) = \infty

= \frac{6}{ln ^{3} ( 2 )} \cdot \frac{1}{\infty}

Vereinfache

\frac{6}{ln ^{3} ( 2 )} \cdot \frac{1}{\infty} : 0

= 0

Graph

Beliebte Beispiele

limit as x approaches-1 of (3+x)/(x^2-1)

x \to - 1 lim (\frac{3 + x}{x ^{2} - 1})

integral of e^{-3x}cos(4x)

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integral of (9x^5-3x^2+7)

\int (9 x^{5} - 3 x^{2} + 7) d x

integral of tan^3(3x)sec(3x)

\int tan^{3} (3 x) sec (3 x) d x

integral of (2x+6)/(x^2+1)

\int \frac{2 x + 6}{x ^{2} + 1} d x