limit as x approaches 0+of x/(x-ln(x))

Lösung

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

0

Schritte zur Lösung

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

mit Einschränkung des unbestimmten Ausdrucks

= \frac{lim _{x \to 0 +} ( x )}{lim _{x \to 0 +} ( x - ln ( x ) )}

x \to 0 + lim (x) = 0

x \to 0 + lim (x - ln (x)) = \infty

= \frac{0}{\infty}

Wende die Unendlichkeitseigenschaft an:

\frac{0}{\infty} = 0

= 0

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