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

Lösung

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

0

Schritte zur Lösung

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

Wende Exponentenregel an:

a^{n} \cdot b^{n} = (a \cdot b)^{n}

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

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

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

mit Einschränkung des unbestimmten Ausdrucks

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

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{1}{x ^{2}}}))^{2}

Vereinfache

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

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

Setze den Wert

x = 0

ein

= (- 0)^{2}

Vereinfache

= 0

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

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})