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

Lösung

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

0

Schritte zur Lösung

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

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

= 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}

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

Setze den Wert

x = 0

ein

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

Vereinfache

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

= 0

x \to (1) lim (\frac{x ^{8} - 1}{x ^{5} - 1})

\int \frac{6 ( 1 + s )}{s ( s ^{2} + 7 s + 6 )} d s

\int 1 - z^{2}

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

x \to 0 lim (\frac{x}{sin ( 5 x )})