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Beliebt Rechnen >

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

Lösung

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

Lösung

0

Schritte zur Lösung

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

Teile durch den größten gemeinsamen Potenznenner:

\frac{\frac{1}{x ^{2}} + \frac{3}{x ^{3}}}{2 - \frac{5}{x ^{3}}}

= x \to \infty lim (\frac{\frac{1}{x ^{2}} + \frac{3}{x ^{3}}}{2 - \frac{5}{x ^{3}}})

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} ( \frac{1}{x ^{2}} + \frac{3}{x ^{3}} )}{lim _{x \to \infty} ( 2 - \frac{5}{x ^{3}} )}

x \to \infty lim (\frac{1}{x ^{2}} + \frac{3}{x ^{3}}) = 0

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

= \frac{0}{2}

Wende Regel an

\frac{0}{a} = 0, a \neq = 0

= 0

Graph

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