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

Lösung

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

\infty

Schritte zur Lösung

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

Umformung für L'Hopital

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

Wende das L'Hopital Theorem an

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

Vereinfache

\frac{- \frac{e ^{\frac{1}{x}}}{x ^{2}}}{- \frac{1}{x ^{2}}} : e^{\frac{1}{x}}

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

Wende die Kettenregel für Grenzen an:

\infty

= \infty

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