limit as t approaches 0+of 2/t-1/(e^t-1)

Lösung

t \to 0 + lim (\frac{2}{t} - \frac{1}{e ^{t} - 1})

\infty

Schritte zur Lösung

t \to 0 + lim (\frac{2}{t} - \frac{1}{e ^{t} - 1})

\frac{2}{t} - \frac{1}{e ^{t} - 1} = \frac{2}{t} (1 - \frac{\frac{1}{e ^{t} - 1}}{\frac{2}{t}})

= t \to 0 + lim (\frac{2}{t} (1 - \frac{\frac{1}{e ^{t} - 1}}{\frac{2}{t}}))

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

= 2 \cdot t \to 0 + lim (\frac{1}{t} (1 - \frac{\frac{1}{e ^{t} - 1}}{\frac{2}{t}}))

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

= 2 \cdot t \to 0 + lim (\frac{1}{t}) \cdot t \to 0 + lim (1 - \frac{\frac{1}{e ^{t} - 1}}{\frac{2}{t}})

t \to 0 + lim (\frac{1}{t}) = \infty

t \to 0 + lim (1 - \frac{\frac{1}{e ^{t} - 1}}{\frac{2}{t}}) = \frac{1}{2}

= 2 \cdot \infty \cdot \frac{1}{2}

Wende die Unendlichkeitseigenschaft an:

c \cdot \infty = \infty

= \infty

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

x \to 2 lim (4 x + 3)

x \to 2 lim (4 x + 2)

x \to 0 lim (6 tan (x))

x \to 8 lim (\frac{4 x - 2}{9})