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

Lösung

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

\infty

Schritte zur Lösung

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

\frac{ln ^{2} ( x )}{x} = ln^{2} (x) \frac{1}{x}

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

mit Einschränkung des unbestimmten Ausdrucks

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

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

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

= \infty \cdot \infty

Wende die Unendlichkeitseigenschaft an:

\infty \infty = \infty

= \infty

x \to 1000 lim (3^{l n (x)})

x \to 0 lim (\frac{\frac{19}{x + 20} - \frac{19}{20}}{x})

x \to 1 + lim (\frac{3 x + 1}{x - 2})

x \to 3 lim (\frac{x ^{2} - 8}{x + 2})

x \to 1 lim (e^{- x^{2}})