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Beliebt Rechnen >

limit as h approaches 0 of ((x+h)^{2/3}-(x^{2/3}))/h

Lösung

h \to 0 lim \frac{( x + h ) ^{\frac{2}{3}} - ( x ^{\frac{2}{3}} )}{h}

Lösung

\frac{2}{3 x ^{\frac{1}{3}}}

Schritte zur Lösung

h \to 0 lim (\frac{( x + h ) ^{\frac{2}{3}} - x ^{\frac{2}{3}}}{h})

Wende das L'Hopital Theorem an

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

Setze den Wert

h = 0

ein

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

Vereinfache

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

Graph

Beliebte Beispiele

integral from b to 2b of x^5

\int_{b}^{2 b} x^{5} d x

integral of ((x^2+1)/(sqrt(x)))

\int (\frac{x ^{2} + 1}{x}) d x

x^2y^{''}-7xy^'+16y=0

x^{2} y^{^{''}} - 7 x y^{^{'}} + 16 y = 0

fläche y=-3x^3+x^2+10x,x>= 0

a re a y = - 3 x^{3} + x^{2} + 10 x, x \geq 0

y^{''}-2y^'-3y=xe^x

y^{^{''}} - 2 y^{^{'}} - 3 y = x e^{x}