limit as x approaches+0 of (e^{-5x}-1)/x

Lösung

x \to + 0 lim (\frac{e ^{- 5 x} - 1}{x})

- 5

Schritte zur Lösung

x \to 0 lim (\frac{e ^{- 5 x} - 1}{x})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{- 5 e ^{- 5 x}}{1})

Setze den Wert

x = 0

ein

= \frac{- 5 e ^{- 5 \cdot 0}}{1}

Vereinfache

= - 5

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