limit as x approaches 0+of 3xln(1/x)

Lösung

x \to 0 + lim (3 x ln (\frac{1}{x}))

0

Schritte zur Lösung

x \to 0 + lim (3 x ln (\frac{1}{x}))

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

= 3 \cdot x \to 0 + lim (x ln (\frac{1}{x}))

Umformung für L'Hopital

= 3 \cdot x \to 0 + lim (\frac{ln ( \frac{1}{x} )}{\frac{1}{x}})

Wende das L'Hopital Theorem an

= 3 \cdot x \to 0 + lim (\frac{- \frac{1}{x}}{- \frac{1}{x ^{2}}})

Vereinfache

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

= 3 \cdot x \to 0 + lim (x)

Setze den Wert

x = 0

ein

= 3 \cdot 0

Vereinfache

= 0

x \to 1 lim (x^{2} - 4 x + 5)

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

x \to 0 lim ((1 - cos (x))^{x})

x \to 1 lim (x - 4)

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