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Beliebt Rechnen >

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

Lösung

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

Lösung

- \infty

Schritte zur Lösung

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

Wende Exponentenregel an:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{x e ^{\frac{1}{x}}} = e^{- \frac{1}{x}} \frac{1}{x}

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

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

mit Einschränkung des unbestimmten Ausdrucks

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

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

x \to 0 - lim (\frac{1}{x}) = - \infty

= \infty \cdot (- \infty)

Wende die Unendlichkeitseigenschaft an:

\infty (- \infty) = - \infty

= - \infty

Graph

Beliebte Beispiele

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\frac{d}{d x} (sec^{2} (x) + csc^{2} (x))

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