limit as x approaches 0+of xln(x^8)

Lösung

x \to 0 + lim (x ln (x^{8}))

0

Schritte zur Lösung

x \to 0 + lim (x ln (x^{8}))

ln (x^{8}) = 8 ln (x)

= x \to 0 + lim (x \cdot 8 ln (x))

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

= 8 \cdot x \to 0 + lim (x ln (x))

Umformung für L'Hopital

= 8 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

Wende das L'Hopital Theorem an

= 8 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{1}{x ^{2}}})

Vereinfache

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

= 8 \cdot x \to 0 + lim (- x)

Setze den Wert

x = 0

ein

= 8 (- 0)

Vereinfache

= 0

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

\frac{\partial}{\partial y} (sin (x^{3} + y^{2}))

\frac{d}{d x} (\frac{3 x + 1}{x + 1})

in v erse l a pl a ce \frac{2}{s ^{2} - 2 s + 9}

y^{^{''}} + 2 y^{^{'}} + y = x^{- 4} e^{- x}