limit as x approaches 0 of (ln(10x+1))/x

Lösung

x \to 0 lim (\frac{ln ( 10 x + 1 )}{x})

10

Schritte zur Lösung

x \to 0 lim (\frac{ln ( 10 x + 1 )}{x})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{\frac{10}{10 x + 1}}{1})

Setze den Wert

x = 0

ein

= \frac{\frac{10}{10 \cdot 0 + 1}}{1}

Vereinfache

= 10

x \to 0 lim (1 - \frac{tan ( 3 x )}{x})

x \to 4 + lim (10 - 2 x)

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

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

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