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

Lösung

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

0

Schritte zur Lösung

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

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

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

Vereinfache

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

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

Setze den Wert

x = 0

ein

= - \frac{3 \cdot 0 ^{2}}{2}

Vereinfache

= 0

x \to 0 lim (ln (1 - e^{- x}))

x \to 5 lim (x^{2} - 4 x + 3)

x \to 0 lim (\frac{e ^{x} - 1 - x}{x})

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

x \to - 1 lim ([x] + [- x])