limit as x approaches 0+of (5x^2)(ln(x))

Lösung

x \to 0 + lim ((5 x^{2}) (ln (x)))

0

Schritte zur Lösung

x \to 0 + lim (5 x^{2} ln (x))

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

= 5 \cdot x \to 0 + lim (x^{2} ln (x))

Umformung für L'Hopital

= 5 \cdot x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x ^{2}}})

Wende das L'Hopital Theorem an

= 5 \cdot x \to 0 + lim (\frac{\frac{1}{x}}{- \frac{2}{x ^{3}}})

Vereinfache

\frac{\frac{1}{x}}{- \frac{2}{x ^{3}}} : - \frac{x ^{2}}{2}

= 5 \cdot x \to 0 + lim (- \frac{x ^{2}}{2})

Setze den Wert

x = 0

ein

= 5 (- \frac{0 ^{2}}{2})

Vereinfache

5 (- \frac{0 ^{2}}{2}) : 0

= 0

t an g e n t y = \frac{x ^{2} - 1}{x ^{2} + x + 1}, at x = 1

\int 4 - 4 sin (x) + sin^{2} (x) d x

\int 64 - 3 x^{2} d x

\frac{\partial}{\partial x} (x^{2} e^{2})

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