limit as x approaches 0 of (ln(1+ax))/x

Lösung

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

a

Schritte zur Lösung

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

Wende das L'Hopital Theorem an

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

Setze den Wert

x = 0

ein

= \frac{\frac{a}{1 + a \cdot 0}}{1}

Vereinfache

= a

x \to \frac{π}{2} lim (\frac{tan ( x )}{x})

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

x \to 2 lim (\frac{5 x}{4 - x ^{2}})

x \to 5 lim (x^{2} - 3)

l h o p i t a l x \to \infty lim (x ln (1 + \frac{3}{x}))