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Beliebt Rechnen >

limit as x approaches 0+of xe^{1/x}

Lösung

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

Lösung

\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

Graph

Beliebte Beispiele

tangent x^3+x^2+5x-1

t an g e n t x^{3} + x^{2} + 5 x - 1

integral of 3^{2x}e^x

\int 3^{2 x} e^{x} d x

limit as x approaches-4 of |x|

x \to - 4 lim (∣ x ∣)

derivative of ln(x^3+4)

\frac{d}{d x} (ln (x^{3} + 4))

y^{^{'}} = 2 cos (5 x)