limit as x approaches 0+of 2xln(1/x)

Lösung

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

0

Schritte zur Lösung

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

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

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

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

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

Vereinfache

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

= 2 \cdot x \to 0 + lim (x)

Setze den Wert

x = 0

ein

= 2 \cdot 0

Vereinfache

= 0

x \to \frac{1}{4} lim (ln (x))

x \to 0 lim (1 - 5 x^{3})

x \to 0 lim (\frac{x ^{4} - 2}{x ^{3}})

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

x \to 4 lim (4 x^{3} - 3 x^{2} + 1)