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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{2}

+1

Dezimale

0.5

Schritte zur Lösung

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

Vereinfache

\frac{1}{t} - \frac{1}{e ^{t} - 1} : \frac{e ^{t} - 1 - t}{t ( e ^{t} - 1 )}

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

Wende das L'Hopital Theorem an

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

Wende das L'Hopital Theorem an

= t \to 0 lim (\frac{e ^{t}}{e ^{t} t + 2 e ^{t}})

Setze den Wert

t = 0

ein

= \frac{e ^{0}}{e ^{0} \cdot 0 + 2 e ^{0}}

Vereinfache

= \frac{1}{2}

Graph

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