limit as x approaches 0+of xln(x^3)

Lösung

x \to 0 + lim (x ln (x^{3}))

0

Schritte zur Lösung

x \to 0 + lim (x ln (x^{3}))

ln (x^{3}) = 3 ln (x)

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

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

Vereinfache

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

= 3 \cdot x \to 0 + lim (- x)

Setze den Wert

x = 0

ein

= 3 (- 0)

Vereinfache

= 0

\frac{\partial}{\partial x} (\frac{2 x ^{2}}{y ^{2} + x ^{2}})

\int_{- 1}^{3} 2 x + 3 - x^{2} d x

\frac{d}{d x} ((arctan (6 x))^{2})

x \to 0 lim (\frac{6 x ^{2} + 6 x}{x})

d er i v a t i v e f (x) = 4 x^{- \frac{1}{8}}