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Beliebt Rechnen >

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

Lösung

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

Lösung

2

Schritte zur Lösung

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

Multipliziere aus

\frac{1 + 3 x + 2 x ^{3}}{x ^{3}} : \frac{1}{x ^{3}} + \frac{3}{x ^{2}} + 2

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

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

mit Einschränkung des unbestimmten Ausdrucks

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

x \to \infty lim (\frac{1}{x ^{3}}) = 0

x \to \infty lim (\frac{3}{x ^{2}}) = 0

x \to \infty lim (2) = 2

= 0 + 0 + 2

Vereinfache

= 2

Graph

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