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Beliebt Rechnen >

limit as x approaches a of (\sqrt[3]{x}-\sqrt[3]{a})/(x^2-a^2)

Lösung

x \to a lim (\frac{3 x - 3 a}{x ^{2} - a ^{2}})

Lösung

\frac{1}{6 a ^{\frac{5}{3}}}

Schritte zur Lösung

x \to a lim (\frac{3 x - 3 a}{x ^{2} - a ^{2}})

Wende das L'Hopital Theorem an

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

Setze den Wert

x = a

ein

= \frac{\frac{1}{3 a ^{\frac{2}{3}}}}{2 a}

Vereinfache

\frac{\frac{1}{3 a ^{\frac{2}{3}}}}{2 a} : \frac{1}{6 a ^{\frac{5}{3}}}

= \frac{1}{6 a ^{\frac{5}{3}}}

Graph

Beliebte Beispiele

sum from y=0 to infinity of 2^{-2-y+x}

y = 0 \sum \infty 2^{- 2 - y + x}

(\partial)/(\partial y)(xsqrt(1+y^5))

\frac{\partial}{\partial y} (x 1 + y^{5})

integral of te^{-at}

\int t e^{- a t} d t

6t^2y^{''}-12y=14t^2-1

6 t^{2} y^{^{''}} - 12 y = 14 t^{2} - 1

integral of 4x^3-10x

\int 4 x^{3} - 10 x d x