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

Lösung

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

0

Schritte zur Lösung

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

ln (x^{2}) = 2 ln (x)

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

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

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

Vereinfache

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

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

Setze den Wert

x = 0

ein

= 2 (- \frac{0 ^{2}}{2})

Vereinfache

2 (- \frac{0 ^{2}}{2}) : 0

= 0

x \to 0 lim (x \frac{1}{x})

x \to 0 lim (tan (x) (ln (x)))

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

x \to 1 lim (2 - \frac{2}{x})

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