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

Lösung

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

0

Schritte zur Lösung

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

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

mit Einschränkung des unbestimmten Ausdrucks

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

x \to 0 lim (e) = e

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

= e - e

Vereinfache

= 0

x \to 4 lim ((4 - x) ln (x - 4))

x \to 0 + lim (\frac{x}{tan ( x )})

x \to 1 lim (sin (1))

x \to - \infty lim (6 (x))

x \to 0 lim (\frac{1}{x} ln (1 + 2 x))