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Beliebt Rechnen >

limit as x approaches 0+of sqrt(x)ln(3x)

Lösung

x \to 0 + lim (x ln (3 x))

Lösung

0

Schritte zur Lösung

x \to 0 + lim (x ln (3 x))

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

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

Vereinfache

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

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

Setze den Wert

x = 0

ein

= - 2 \cdot 0^{\frac{1}{2}}

Vereinfache

= 0

Graph

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