limit as x approaches 0 of (\sqrt[3]{x+1}+x-1)/x

Lösung

x \to 0 lim (\frac{3 x + 1 + x - 1}{x})

\frac{4}{3}

Dezimale

1.33333 \dots

Schritte zur Lösung

x \to 0 lim (\frac{3 x + 1 + x - 1}{x})

Wende das L'Hopital Theorem an

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

Setze den Wert

x = 0

ein

= \frac{\frac{1}{3 ( 0 + 1 ) ^{\frac{2}{3}}} + 1}{1}

Vereinfache

\frac{\frac{1}{3 ( 0 + 1 ) ^{\frac{2}{3}}} + 1}{1} : \frac{4}{3}

= \frac{4}{3}

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