limit as x approaches 0+of x^{1/4}*ln(x)

Lösung

x \to 0 + lim (x^{\frac{1}{4}} \cdot ln (x))

0

Schritte zur Lösung

x \to 0 + lim (x^{\frac{1}{4}} ln (x))

Umformung für L'Hopital

= x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x ^{\frac{1}{4}}}})

Wende das L'Hopital Theorem an

= x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{4 x ^{\frac{5}{4}}}})

Vereinfache

\frac{\frac{1}{x}}{- \frac{1}{4 x ^{\frac{5}{4}}}} : - 4 x^{\frac{1}{4}}

= x \to 0 + lim (- 4 x^{\frac{1}{4}})

Setze den Wert

x = 0

ein

= - 4 \cdot 0^{\frac{1}{4}}

Vereinfache

= 0

x \to 2 - lim (F (x))

x \to \infty lim (\frac{x}{4 x})

x \to \infty lim ([0, + x])

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

x \to \frac{π}{2} lim (cot^{2} (x))