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Beliebt Rechnen >

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

Lösung

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

Lösung

0

Schritte zur Lösung

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

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

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

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

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

Vereinfache

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

= x \to 0 + lim (- x)

Setze den Wert

x = 0

ein

= - 0

Vereinfache

= 0

Graph

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