limit as x approaches 0+of x(ln(x))^2

Lösung

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

0

Schritte zur Lösung

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

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

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

Vereinfache

\frac{\frac{2 l n ( x )}{x}}{- \frac{1}{x ^{2}}} : - 2 x ln (x)

= x \to 0 + lim (- 2 x ln (x))

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

= - 2 \cdot x \to 0 + lim (x ln (x))

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

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

Vereinfache

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

= - 2 \cdot x \to 0 + lim (- x)

Setze den Wert

x = 0

ein

= - 2 (- 0)

Vereinfache

= 0

\frac{d}{d x} (\frac{( - 4 x ) ( 2 x - 2 )}{- 3 x ^{2} + 1})

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

\frac{d}{d x} ((x y^{3} + x^{2} y)^{3})

\int \frac{1}{9 x + 7} d x

\frac{d}{d x} (\frac{1}{3 ( x - 1 ) ^{\frac{2}{3}}})