limit as x approaches 1 of (\sqrt[4]{x}-1)/(\sqrt[5]{x)-1}

Lösung

x \to 1 lim (\frac{4 x - 1}{5 x - 1})

\frac{5}{4}

Dezimale

1.25

Schritte zur Lösung

x \to 1 lim (\frac{4 x - 1}{5 x - 1})

Wende das L'Hopital Theorem an

= x \to 1 lim (\frac{\frac{1}{4 x ^{\frac{3}{4}}}}{\frac{1}{5 x ^{\frac{4}{5}}}})

Setze den Wert

x = 1

ein

= \frac{\frac{1}{4 \cdot 1 ^{\frac{3}{4}}}}{\frac{1}{5 \cdot 1 ^{\frac{4}{5}}}}

Vereinfache

\frac{\frac{1}{4 \cdot 1 ^{\frac{3}{4}}}}{\frac{1}{5 \cdot 1 ^{\frac{4}{5}}}} : \frac{5}{4}

= \frac{5}{4}

x \to 3 lim (\frac{( x ^{2 - 7 x + 12} )}{( 3 - x )})

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

x \to \infty lim (- 2 x e^{- 2 x})

d er i v a t i v e y = \frac{1}{2 cos ^{2} ( x )}

i = 0 \sum \infty \frac{i}{2 ^{i}}