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Beliebt Rechnen >

limit as x approaches infinity of (\sqrt[3]{x}+5x+3)/(-2x+x^{2/3)+7}

Lösung

x \to \infty lim (\frac{3 x + 5 x + 3}{- 2 x + x ^{\frac{2}{3}} + 7})

Lösung

- \frac{5}{2}

+1

Dezimale

- 2.5

Schritte zur Lösung

x \to \infty lim (\frac{3 x + 5 x + 3}{- 2 x + x ^{\frac{2}{3}} + 7})

Teile durch den größten gemeinsamen Potenznenner:

\frac{\frac{1}{x ^{\frac{2}{3}}} + 5 + \frac{3}{x}}{- 2 + \frac{1}{x ^{\frac{1}{3}}} + \frac{7}{x}}

= x \to \infty lim (\frac{\frac{1}{x ^{\frac{2}{3}}} + 5 + \frac{3}{x}}{- 2 + \frac{1}{x ^{\frac{1}{3}}} + \frac{7}{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{lim _{x \to \infty} ( \frac{1}{x ^{\frac{2}{3}}} + 5 + \frac{3}{x} )}{lim _{x \to \infty} ( - 2 + \frac{1}{x ^{\frac{1}{3}}} + \frac{7}{x} )}

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

x \to \infty lim (- 2 + \frac{1}{x ^{\frac{1}{3}}} + \frac{7}{x}) = - 2

= \frac{5}{- 2}

Vereinfache

= - \frac{5}{2}

Graph

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