limit as x approaches 0 of 1/x ln(1+2x)

Lösung

x \to 0 lim (\frac{1}{x} ln (1 + 2 x))

2

Schritte zur Lösung

x \to 0 lim (\frac{1}{x} ln (1 + 2 x))

Vereinfache

\frac{1}{x} ln (1 + 2 x) : \frac{ln ( 1 + 2 x )}{x}

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

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{\frac{2}{1 + 2 x}}{1})

Setze den Wert

x = 0

ein

= \frac{\frac{2}{1 + 2 \cdot 0}}{1}

Vereinfache

= 2

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

x \to 0 - lim (2 + e^{\frac{1}{x}})

x \to 2 lim (1776)

x \to 0 lim (\frac{4 x}{x ^{2} + x})

x \to - 4 lim (x^{2} + 9)