limit as x approaches 0 of (e^x-1)/(12x)

Lösung

x \to 0 lim (\frac{e ^{x} - 1}{12 x})

\frac{1}{12}

Dezimale

0.08333 \dots

Schritte zur Lösung

x \to 0 lim (\frac{e ^{x} - 1}{12 x})

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

= \frac{1}{12} \cdot x \to 0 lim (\frac{e ^{x} - 1}{x})

Wende das L'Hopital Theorem an

= \frac{1}{12} \cdot x \to 0 lim (\frac{e ^{x}}{1})

Setze den Wert

x = 0

ein

= \frac{1}{12} \cdot \frac{e ^{0}}{1}

Vereinfache

\frac{1}{12} \cdot \frac{e ^{0}}{1} : \frac{1}{12}

= \frac{1}{12}

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