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

Lösung

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

0

Schritte zur Lösung

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

Vereinfache

x ln (\frac{1}{x ^{2}}) : - x ln (x^{2})

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

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

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

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

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

Vereinfache

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

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

Setze den Wert

x = 0

ein

= - (- 2 \cdot 0)

Vereinfache

= 0

x \to 2 lim (3 + x - 2)

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

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

x \to 2 lim (\frac{1}{x + 3} + 5)

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