limit as x approaches 0+of x^2ln(x^3)

Lösung

x \to 0 + lim (x^{2} ln (x^{3}))

0

Schritte zur Lösung

x \to 0 + lim (x^{2} ln (x^{3}))

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

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

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

= 3 \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}

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

Setze den Wert

x = 0

ein

= 3 (- \frac{0 ^{2}}{2})

Vereinfache

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

= 0

x \to \infty lim (\frac{x ^{2} - 5 x + 4}{4 x ^{2} + 2 x})

x \to \infty lim (- \frac{x}{0})

h \to 0 lim (csc (h) - cot (h))

x \to - 3 lim ((4 x - 2 \cdot 3)^{2})

x \to 0 + lim (5 x ln (x))