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Beliebt Rechnen >

limit as x approaches 0+of xln(x^4)

Lösung

x \to 0 + lim (x ln (x^{4}))

Lösung

0

Schritte zur Lösung

x \to 0 + lim (x ln (x^{4}))

ln (x^{4}) = 4 ln (x)

= x \to 0 + lim (x \cdot 4 ln (x))

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

= 4 \cdot x \to 0 + lim (x ln (x))

Umformung für L'Hopital

= 4 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

Wende das L'Hopital Theorem an

= 4 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

Vereinfache

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

= 4 \cdot x \to 0 + lim (- x)

Setze den Wert

x = 0

ein

= 4 (- 0)

Vereinfache

= 0

Graph

Beliebte Beispiele

integral from-2 to 3 of (26)/(x^4)

\int_{- 2}^{3} \frac{26}{x ^{4}} d x

derivative of 1/(1+x^4)

\frac{d}{d x} (\frac{1}{1 + x ^{4}})

derivative of 4sec(x-8cos(x))

\frac{d}{d x} (4 sec (x) - 8 cos (x))

fläche y=x^3,y=x,x>= 0

a re a y = x^{3}, y = x, x \geq 0

integral from 0 to 1 of x^9e^{x^5}

\int_{0}^{1} x^{9} e^{x^{5}} d x