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Beliebt Rechnen >

limit as x approaches infinity of (2x^3+3x-4)/(5-4x^3)

Lösung

x \to \infty lim (\frac{2 x ^{3} + 3 x - 4}{5 - 4 x ^{3}})

Lösung

- \frac{1}{2}

+1

Dezimale

- 0.5

Schritte zur Lösung

x \to \infty lim (\frac{2 x ^{3} + 3 x - 4}{5 - 4 x ^{3}})

Teile durch den größten gemeinsamen Potenznenner:

\frac{2 + \frac{3}{x ^{2}} - \frac{4}{x ^{3}}}{\frac{5}{x ^{3}} - 4}

= x \to \infty lim (\frac{2 + \frac{3}{x ^{2}} - \frac{4}{x ^{3}}}{\frac{5}{x ^{3}} - 4})

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{lim _{x \to \infty} ( 2 + \frac{3}{x ^{2}} - \frac{4}{x ^{3}} )}{lim _{x \to \infty} ( \frac{5}{x ^{3}} - 4 )}

x \to \infty lim (2 + \frac{3}{x ^{2}} - \frac{4}{x ^{3}}) = 2

x \to \infty lim (\frac{5}{x ^{3}} - 4) = - 4

= \frac{2}{- 4}

Vereinfache

\frac{2}{- 4} : - \frac{1}{2}

= - \frac{1}{2}

Graph

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