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Beliebt Rechnen >

limit as x approaches infinity of (4x^2+5x)/(sqrt(10+x^4))

Lösung

x \to \infty lim (\frac{4 x ^{2} + 5 x}{10 + x ^{4}})

Lösung

4

Schritte zur Lösung

x \to \infty lim (\frac{4 x ^{2} + 5 x}{10 + x ^{4}})

Multipliziere aus

\frac{4 x ^{2} + 5 x}{10 + x ^{4}} : \frac{4 x ^{2}}{10 + x ^{4}} + \frac{5 x}{10 + x ^{4}}

= x \to \infty lim (\frac{4 x ^{2}}{10 + x ^{4}} + \frac{5 x}{10 + x ^{4}})

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{4 x ^{2}}{10 + x ^{4}}) + x \to \infty lim (\frac{5 x}{10 + x ^{4}})

x \to \infty lim (\frac{4 x ^{2}}{10 + x ^{4}}) = 4

x \to \infty lim (\frac{5 x}{10 + x ^{4}}) = 0

= 4 + 0

Vereinfache

= 4

Graph

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